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PUBLICATION LIST

[1] Harris, M.: Systematic growth of Mordell-Weil groups of abelian
varieties in towers of number fields. *Inventiones Math.***51**, 123-141 (1979).

[2] Harris, M.: A note on three
lemmas of Shimura. *Duke Math. J.* **46**, 871-879 (1979).

[3] Harris, M.: P-adic
representations arising from descent on abelian varieties. *Compositio Math.*
**39**,
177-245 (1979); Correction, Compositio Math. (2000).

The principal error in this paper
was the incorrect claim that Iwasawa's sufficient criterion for a compact L-module to be torsion — that its group of
coinvariants be finite — generalizes to the non-abelian situation. A correct
criterion, involving the Euler characteristic, has since been found by Susan
Howson. Several proofs based on the fallacious criterion are replaced by
alternative proofs in the Correction. However, in the absence of a valid
criterion, it is impossible to justify the claim that certain modules
constructed from Selmer groups of elliptic curves are torsion L-module. Using the Euler
characteristic criterion, Coates and Howson found the first examples of torsion
modules over the Iwasawa algebra of GL(2,**Z**_{p})
coming from Selmer groups of elliptic curves.

To my knowledge,the remainder of
the results of this paper are correct, when taken in conjunction with the
correction. This includes some of the basic structural theory of compact L-modules in the non-abelian case, the proof
that the L-module
constructed from ideal class groups (the direct analogue of the module studied
by Iwasawa) is torsion, and certain control theorems.

[4] Harris, M.: Kubert-Lang units
and elliptic curves without complex multiplication. *Compositio Math. ***41**, 127-136 (1980).

[RETRACTED]
Harris, M.: The annihilators of p-adic induced modules. *J. of Algebra*
**67**,
68-71 (1980). NOTE: Jordan Ellenberg has found a fatal flaw in the
main argument, so this paper should be disregarded. The problem is the
deduction on lines -2 and -3 of p. 69, which is
not justified. Ardakov and Wadsley have now shown (arXiv:1308.5104) that
the main result is false for every semisimple p-adic group.

[5] Harris, M.: The rationality
of holomorphic Eisenstein series. *Inventiones Math.* **63**, 305-310 (1981).

[6] Harris, M.: Special values of
zeta functions attached to Siegel modular forms. *Annales Scient. de l'Ec. Norm. Sup. ***14**, 77-120
(1981).

A rumor has been circulating to the
effect that one of the statements used in this article was not proved until
several years later, and that the proofs are
therefore incomplete. Apparently this is based on a misunderstanding. The
statement in question, as far as I can tell, is 3.6.2, the claim that the
antiholomorphic highest weight module for Sp(2n) is
irreducible down to weight n/2. This is of course a simple consequence of
the unitarity of the module (cited in 3.6.1), the fact that it is generatedby a
highest weight vector, and the well known fact that any submodule is generated
by highest weight vectors. If there is anything more to the rumor I
don't know what it is.

[7] Harris, M.: Maass operators
and Eisenstein series. *Math. Ann. ***258**, 135-144 (1981).

[8] Harris, M.: P-adic measures
for spherical representations of reductive p-adic groups. *Duke Math. J. ***49**, 497-512 (1982).

[9] Harris, M., Jakobsen, H.P.:
Singular holomorphic representations and singular modular forms. *Math. Ann.* **259**,
227-244 (1982).

[10] Harris, M., Jakobsen, H.P.:
Covariant differential operators, in Group Theoretical Methods in Physics
(Istanbul, 1982), *Lecture Notes in Physics*, **180**, 16-34. Berlin:
Springer-Verlag (1983).

[11] Harris, M.: Eisenstein
series on Shimura varieties. *Ann. of Math.* **119**, 59-94 (1984).

[12] Harris, M.: Arithmetic
vector bundles on Shimura varieties, in Automorphic Forms of Several
Variables, Proceedings of the Taniguchi Symposium, Katata, 1983 ,
138-159. Boston: Birkhaüser (1984).

The argument in 3.5 of this mainly
expository paper, concerning jet bundles, is nonsense. A correct argument
is given in the subsequent articles.

[13] Harris, M.: Arithmetic
vector bundles and automorphic forms on Shimura varieties. I. *Inventiones Math.*
**82**,
151-189 (1985).

The term "arithmetic vector
bundle" has since been replaced by "automorphic vector bundle".
The argument in (3.6.7), deriving existence of a
model over a number field of an "absolutely arithmetic" automorphic
vector bundle by means of a cocycle condition involving Aut(**C**), needs
further justification. [SEE NOTE BELOW.] A simpler alternative is to observe
that a quotient of the canonical principal bundle I(G,X) by a finite subgroup C
of the center of G is already defined over the
reflex field E(G,X). One can take C to be the intersection of the center
of G with the derived subgroup G^{der}. Indeed, the fact that the
quotient of I(G,X) by the center of G is defined over E(G,X) follows from
Proposition 3.7, whereas the fact that the quotient by G^{der} is
defined over E(G,X) is a conseqence of the theory for tori. Since finite
étale covers are defined over finite algebraic extensions, one sees immediately
that I(G,X) is defined over some number field, as are the Hecke correspondences
on I(G,X). One can then replace the cocycle

for Aut(**C**) by a continuous cocycle on the Galois group
of the algebraic closure of **Q**. A complete argument may be given elsewhere.

NOTE ADDED MARCH 21,
2008: After rereading Shimura's original proof of the existence of
canonical models

using cocycles on Aut(**C**) [Shimura, *Annals of Math.***, 83 **(1966) 294-338] in the light of its reformulation by

Varshavsky [Appendix to *Selecta Math.*,
**8 **(2002) 283-314], I am now
convinced that the argument in (3.6.7) is essentially correct.

The argument proceeds by constructing a cocycle on Aut(**C**) with values in **G**m
that is shown to be effective for descending to

an appropriate reflex field an automorphic vector bundle on the Shimura variety
attached to a torus. It thus necessarily

satisfies the required continuity property. All that is missing from the
proof is acknowledgment of of this requirement.

[14] Harris, M.: Arithmetic
vector bundles and automorphic forms on Shimura varieties II. *Compositio Math*.
**60**,
323-378 (1986).

[15] Harris, M., Phong, D. H.:
Cohomologie de Dolbeault à croissance logarithmique à l'infini. *C. R. Acad. Sci.
Paris***
302**, 307-310 (1986).

José Ignacio Burgos pointed
out in 1997 that the argument in Griffiths-Harris, used to extend the Poincaré
Lemma with logarithmic singularities from the one-dimensional case to the
general case, does not apply in the present situation. Briefly, the
Dolbeault complex defined in this paper consists of forms w which, together with their antiholomorphic
derivatives, satisfy logarithmic growth conditions in the neighborhood of a
divisor with normal crossings. However, the Griffiths-Harris argument
introduces additional holomorphic derivatives, which may not belong to the
original complex. The quotation
should have been of the argument used by Borel in reference [1], which is based
on integration rather than differentiation.

As noted in [19], and as observed
independently by Burgos, one can actually reprove the one-dimensional Poincaré
lemma with logarithmic singularities for forms all of whose derivatives,
holomorphic as well as anti-holomorphic, satisfy the growth conditions; this is
even necessary if one wants to obtain Lie algebra cohomology complexes to
calculate the cohomology of Shimura varieties. A complete proof of this
fact, and the correct deduction of the higher-dimensional case, was published
in [42], in response to Burgos' comment.

[16] Harris, M.: Formes
automorphes "géométriques" non-holomorphes: Problèmes
d'arithméticité, in *Sém de Théorie des Nombres, Paris 1984-85* Boston: Birkhaüser
(1986).

[17] Harris, M.:
Arithmetic of the oscillator representation, manuscript (1987), see this page.

[18] Harris, M.: Functorial
properties of toroidal compactifications of locally symmetric varieties, *Proc. Lon. Math.
Soc.* **59**,
1-22 (1989)

[19] Harris, M.: Automorphic
forms and the cohomology of vector bundles on Shimura varieties, in L. Clozel
and J.S. Milne, eds., *Proceedings of the Conference on Automorphic Forms, Shimura Varieties,
and L-functions, Ann Arbor, 1988*, *Perspectives in Mathematics*, New
York: Academic Press, Vol. II, 41-91 (1989).

[20] Harris, M.: Automorphic
forms of d-bar-cohomology type as coherent cohomology classes, *J. Diff. Geom.*
**32**, 1-63
(1990).

[21] Harris, M.: Period
invariants of Hilbert modular forms, I: Trilinear differential operators
and L-functions, in J.-P. Labesse and J. Schwermer, eds., Cohomology of
Arithmetic Groups and Automorphic Forms, Luminy, 1989, *Lecture Notes in Math.*, **1447**,
155-202 (1990).

The last section of this article
assumes the extension of the techniques of [22] to general totally real
fields. At the time of publication, I was under the mistaken impression
that the Siegel-Weil formula for the central value of the Eisenstein series,
proved by Kudla and Rallis, extended in a simple way to the symplectic
similitude group GSp(6). In fact, the extension proposed in [22] only
works over **Q**.
A correct Siegel-Weil formula for similitude groups is proved in [49].
Thus the proofs in this article are now complete.

[22] Harris, M., Kudla, S.: The central
critical value of a triple product L-function, *Ann. of Math*., **133**, 605-672 (1991).

[23] Harris, M., Kudla, S.:
Arithmetic automorphic forms for the non-holomorphic discrete series of GSp(2),
*Duke Math. J. ***66**, 59-121
(1992).

[24] Garrett, P.B., Harris, M.:
Special values of triple product L-functions, *Am. J. Math.* **115**, 159-238 (1993).

[25] Harris, M.:
Non-vanishing of L-functions of 2x2 unitary groups, *Forum Math.* **5**, 405-419 (1993).

[26] Harris, M., Soudry, D., Taylor,
R.: l-adic representations attached to modular forms over an imaginary
quadratic field, I: lifting to GSp(4,**Q**), *Inventiones Math.*, **112**, 377-411 (1993).

On p. 410, lines 2-3, we claim to
have constructed supercuspidal representations of GSp(4) over a p-adic field
that were missed by Vignéras in her article [V]. Dipendra Prasad pointed
out that these supercuspidal representations, and the corresponding
representations of the Weil group, were actually constructed in [V] in a
different matrix representation.

[27] Harris, M.: L-functions of 2
by 2 unitary groups and factorization of periods of Hilbert modular
forms, *J.
Am. Math. Soc.* **6**, 637-719, (1993).

The relation of CM periods to
special values of L-functions of Hecke characters, obtained in general by Blasius,
is quoted on numerous occasions in this article. Unfortunately, it is
quoted here, as in the appendix to [22], with a sign mistake. The final
formulas are indifferent to the choice of sign, so no harm is done. The
mistake is corrected in the introduction to [35], whose results depend on the
correct choice of sign.

[28] Harris, M., Zucker, S.:
Boundary cohomology of Shimura varieties, I: coherent cohomology on
the toroidal boundary, *Annales Scient. de l'Ec. Norm. Sup.* **27**, 249-344 (1994).

[29] Harris, M., Zucker, S.:
Boundary cohomology of Shimura varieties, II: mixed Hodge structures
, *Inventiones
Math.***116**,
243-307 (1994); Erratum, *Inventiones Math.*, **123**, 437 (1995).

[30] Harris, M.: Hodge-de
Rham structures and periods of automorphic forms, in Motives, *Proc. Symp. Pure
Math.. AMS*, **55**, Part 2, pp. 573-624 (1994).

[31] Blasius, D., Harris, M.,
Ramakrishnan, D.: Coherent cohomology, limits of discrete series, and
Galois conjugation, *Duke Math. J, * **73**, 647-686 (1994).

[32] Harris, M.: Period
invariants of Hilbert modular forms, II, *Compositio Math. ***94**, 201-226 (1994).

[33] Harris, M., Kudla, S.,
Sweet, W. J.: Theta dichotomy for unitary groups, *J. Am. Math. Soc.***9**, 941-1004 (1996).

[34] Harris, M.: Supercuspidal
representations in the cohomology of Drinfel'd upper half spaces; elaboration
of Carayol's program, *Inventiones Math.* **129**, 75-119 (1997).

The correction character,
denoted n(Gp) on p. 100, is calculated incorrectly on p. 101. The
correct calculation is given on p. 181 of [37], where the sign convention of
[34] is also replaced by one consistent with the conventions of the book of
Rapoport and Zink.

[35] Harris, M.: L-functions and
periods of polarized regular motives, *J.Reine Angew. Math.***483**, 75-161 (1997).

The main result on special
values of L-functions of automorphic forms on unitary Shimura varieties refers
to an unpublished

calculation of archimedean zeta integrals, due to P.
Garrett (Lemma 3.5.3). Garrett has since written up this calculation in a
more

general setting and his results are included as an
appendix to [53].

[36] Harris, M. , Li,
J.-S.: A Lefschetz property for subvarieties of Shimura varieties, *J. Alg. Geom. ***7**, 77-122
(1998).

[37] Harris, M.: The local
Langlands conjecture for GL(n) of a p-adic field, n < p, *Inventiones Math.*
**134**,
177-210 (1998).

[38] Harris, M.:
Cohomological automorphic forms on unitary groups, I: rationality of the
theta correspondence, *Proc. Symp. Pure Math,* **66.2**, 103-200 (1999).

A great many misprints were
discovered while preparing the sequel [55]. There were also a few
substantial mathematical errors. These were all

corrected in the introduction to [55].

[39] Harris, M.: Galois
properties of cohomological automorphic forms on GL(n), *J. Math. Kyoto Univ. ***39**, 299-318
(1999).

[40] Harris, M., Tilouine, J.:
p-adic measures and square roots of triple product L-functions, *Math. Ann.*, **320**,
127-147 (2001).

A recent article by Darmon and Rotger
has found a different formula for the corrected Euler factor at p in
Proposition 2.2.2. There must

be an error in our (elementary) calculation, but we have not
yet been able to find it.

[41] Harris, M., Scholl, A.: A
note on trilinear forms for reducible representations and Beilinson's
conjectures, *J.
European Math. Soc.*, **3**, 93-104 (2001).

[42] Harris, M., Zucker, S.:
Boundary cohomology of Shimura varieties, III: Coherent cohomology on
higher-rank boundary strata and applications to Hodge theory, *Mémoires de la
SMF,* **85**
(2001).

[43] Harris, M., Taylor, R.: The
geometry and cohomology of some simple Shimura varieties, *Annals of
Mathematics Studies*, **151** (2001).

[44] Harris,
M.: Local Langlands correspondences and vanishing cycles on Shimura
varieties, Proceedings of the European Congress of Mathematics, Barcelona,
2000; *Progress
in Mathematics*, **201**, Basel: Birkhaüser Verlag, 407-427 (2001).

Eva Viehmann has found a mistake in
the statement of Proposition 4.1 (ii), which means that Conjecture 5.2 needs to
be corrected. The statements seem

to be all right for split groups but not in the general
case. Viehmann has proposed a corrected version. See item [51]
below.

[45] Harris, M., Taylor, R.: Regular models of certain Shimura varieties,
*Asian J. Math.***6**, 61-94
(2002).

[46] Harris, M.: On the
local Langlands correspondence, in Proceedings of the International Congress of
Mathematicians, Beijing 2002, Vol II, 583-597.

[47] Harris, M., Taylor, R.:
Deformations of automorphic Galois representations (manuscript, 1998-2003).

[48] Harris, M., Kudla, S.: On a
conjecture of Jacquet, in H. Hida, D. Ramakrishnan, F. Shahidi, eds.,
Contributions to automorphic forms, geometry, and number theory (collection in
honor of J. Shalika's 60th birthday), 355-371 (2004).

[49] Harris, M.:
Occult period invariants and critical values of the degree four L-function of
GSp(4) in H. Hida, D. Ramakrishnan, F. Shahidi, eds.,

Contributions to automorphic forms, geometry, and number theory (collection in
honor of J. Shalika's 60th birthday), 331-354 (2004).

[50] Harris, M., Labesse, J-P.: Conditional base change for
unitary groups, *Asian J. Math*, **8**, 653-684 (2004).

[51] Harris, M.: The Local Langlands correspondence: Notes of
(half) a course at the IHP, Spring 2000, in J. Tilouine, H. Carayol, M.
Harris, M.-F. Vignéras, eds., Formes Automorphes, *Astérisque*, **298**,
17-145 (2005) .

The mistake in [44] arises from an
incorrect argument on pp. 130-131 of this article. Viehmann's corrected
version should appear in her forthcoming work, and I hope to

revise the calculation of the global Galois representation
as a sum of contributions of individual strata.

[52] Harris, M., Li, J.-S., et Skinner, C.: The Rallis inner
product formula and p-adic L-functions, in J. Cogdell et al., eds, Automorphic
Representations, L-functions and Applications: Progress and Prospects,
Berlin: de Gruyter, 225-255 (2005).

[53] Harris, M. : A simple proof of rationality of Siegel-Weil
Eisenstein series, in W.T. Gan, S.S. Kudla, and Y. Tschinkel, eds.,

*Eisenstein Series and Applications*,
Boston: Birkhäuser, *Progress in
Mathematics* **258 **(2008) 149-186
(preceded by appendix by P. Garrett).

[54] Harris, M., Li, J.-S., et Skinner, C.: p-adic L
functions for unitary Shimura varieties, I : Construction of the
Eisenstein measure, *Documenta Math.*, ** **John H.
Coates' Sixtieth Birthday 393-464 (2006).

[55] Harris, M.: Cohomological automorphic forms on unitary
groups, II: period relations and values of L- functions in Li, Tan,
Wallach, and

Zhu, eds., Harmonic Analysis, Group Representations, Automorphic Forms and
Invariant Theory, Vol. 12, Lecture Notes Series, Institute

of Mathematical Sciences, National University of Singapore (volume in honor of
Roger Howe) (2007) 89-150.

[56] Clozel, L., Harris, M., and Taylor, R. : Automorphy for some
l-adic lifts of automorphic mod l Galois representationsm *Publ. Math. IHES*, **108** 1-181 (2008).

[57] Harris, M., Shepherd-Barron, N, and Taylor, R.: A family of Calabi-Yau
varieties and potential automorphy, *Annals
of Math.*, **171**, 779-813
(2010).

[58] Harris, M., Potential automorphy of odd-dimensional symmetric powers
of elliptic curves, and applicationsm in *Algebra,
Arithmetic, and Geometry: In Honor of Yu. I. Manin*,

Vol II, Boston: Birkhäuser, *Progress in Mathematics*, **270**
(2009) 1-23.

[59] Harris, M.: Arithmetic applications of the Langlands program, *Japanese J. Math.*, 3rd ser., **5** (2010) 1-71.

[60] Guralnick, R., Harris, M., Katz, N. : Automorphic realization
of Galois representations, *J. Euro. Math.
Soc.*, **12**, (2010) 915–937.

[61] Harris, M. : Galois representations, automorphic forms, and
the Sato-Tate conjecture., Clay Research Proceedings, 2007, in press.

[62] Harris, M. : An introduction to the stable trace formula, in L.
Clozel, M. Harris, J.-P. Labesse, B. C. Ngô, eds. *The stable trace formula, Shimura varieties, and arithmetic
applications. Volume I: Stabilization of the trace formula*,
Boston: International Press (2011) 3-47.

[63] Clozel, L., Harris, M., Labesse, J.-P.: Endoscopic
transfer, in L. Clozel, M. Harris, J.-P. Labesse, B. C. Ngô, eds. *The stable trace formula, Shimura varieties,
and arithmetic applications. Volume I: Stabilization of the trace formula*,
Boston: International Press (2011) 475-496.

[64] Clozel, L., Harris, M., Labesse, J.-P.: Construction of automorphic
Galois representations, I., in L. Clozel, M. Harris, J.-P. Labesse, B. C. Ngô,
eds. *The stable trace formula, Shimura
varieties, and arithmetic applications. Volume I: Stabilization of the
trace formula*, Boston: International Press (2011) 497-527.

[65] Chenevier, G., Harris, M., Construction of automorphic Galois
representations, II (manuscript 2009-2011).

[66] Harris, M., Li, J.-S.. Sun, Binyong, Theta correspondence for close
unitary groups, *Advanced Lectures in
Mathematics*, special issue in honor of S. Kudla, (2011) 265-308.

[67] Barnet-Lamb, T., Geraghty, D., Harris, M., et Taylor, R. : A
family of Calabi-Yau varieties and potential automorphy II, *Proceedings RIMS*, **47** (2011) 29-98.

[68] Harris, M. : The Taylor-Wiles method for coherent
cohomology, *J. Reine Angew. Math.*, **679** (2013) 125-153.

[69]
Harris, M.: L-functions and periods of adjoint motives, *Algebra and Number Theory*, **7** (2013), 117-155.

[70] Harris, M.: Beilinson-Bernstein localization over **Q** and
periods of automorphic forms,

** International Math. Research Notices**,

[71] Chenevier, G., Harris, M.: Construction of automorphic
Galois representations, II,

** Cambridge Journal of Mathematics**,

**Other
publications**

1. Review of Holomorphic
Hilbert Modular Forms (P. Garrett), *Bull. AMS*, **25**, 184-195 (1991)

2. Contexts of
Justification, *Math.
Intelligencer*, Winter 2001.

3. Review of *Cohomologie,
stabilisation, et changement de base* (J.-P. Labesse), *Gazette des
Mathématiciens,* 2001.

4. Review of *Mathematics and
the Roots of Postmodern Thought *(V. Tasic), *Notices of the AMS*, August 2003 .

5. Review of
Introduction to the Langlands Program (J. Bernstein et S. Gelbart), *Bull. AMS* **41** 257-266 (2004).

6. A sometimes funny book supposedly about infinity, review of *Everything and More* (D.F. Wallace), *Notices of the AMS*, **51**, 632-638, June-July 2004.

7. “Why mathematics?” you might ask, in T. Gowers, ed. *The Princeton
Companion to Mathematics*, Princeton University Press (2008) 966-977.

8. Do Androids Prove
Theorems in Their Sleep?, to appear in A. Doxiadis and B. Mazur, eds, *Circles Disturbed*, Princeton University
Press (2012).