Interview for the seminar Geometry, Arithmetic and Differential Equations of Periods (GADEPs), Rio de Janeiro, Friday, October 9, 2020. The video is available on You Tube.
New call for the Graduate Research Assistantships in Developing Countries (GRAID) program of the International Mathematical Union: Application Deadline March 15, 2021.
AMS 2021 Bertrand Russell Prize.
The prize honors research or service contributions of mathematicians or related professionals to promoting good in the world and recognizes the various ways that mathematics furthers human values.
Interview par le CIMPA le 9 décembre 2020 à Nice.
Archives from January 2009 till now.
April 12 - 23, 2021: Hanoi (Vietnam) (online)
CIMPA School on Functional Equations: Theory, Practice and Interaction.
Introduction to transcendental number theory
Content, with links to the videos; pdf file 2p.
Courses 1 - 5, pdf file 33p.
Course 6,
slides pdf file 52p.
Course 7,
slides pdf file 116p.
Course 8,
slides pdf file (expanded version, 132 pages vs 87 pages).
Exercises pdf file (4 pages).
30 mai 2021, Ultra Trail Tour de Nancy, 43 km.
15-18 juillet 2021. UT4M Challenge 80.
July 30 - August 6, 2021: Popayán (Colombia).
CIMPA School on
isogenies of elliptic curves and their applications to cryptography.
Introductory course on Finite fields.
Universidad del Cauca, Popayán. The school is scheduled July 26 - August 6.
On transcendental entire functions with infinitely many derivatives taking integer values at two points.
31 pages.
Southeast Asian Bulletin of Mathematics, to appear in 2021.
arXiv: 1912.00173 [math.NT].
On transcendental entire functions with infinitely many derivatives taking integer values at finitely many points.
Moscow Journal of Combinatorics and Number Theory,
9-4 (2020), 371--388.
DOI 10.2140/moscow.2020.9.371
arXiv: 1912.00174 [math.NT].
Avec
Etienne Fouvry,
Sur la représentation des entiers par des formes cyclotomiques de grand degré.
Bull. Soc. Math. France, 148 2 (2020), 253-282. DOI 10.24033/bsmf.2805.
arXiv: 1909.01892 [math.NT].
With
Etienne Fouvry and
Claude Levesque,
Representation of integers by cyclotomic binary forms.
Acta Arithmetica, 184.1 (2018), 67 - 86.
DOI 10.4064/aa171012-24-12.
arXiv: 712.09019 [math.NT].
Online Encyclopedia of Integer Sequences:
OEIS A296095 Integers represented by cyclotomic binary forms.
OEIS A293654 Integers not represented by cyclotomic binary forms.
OEIS A299214 Number of representations of integers by cyclotomic binary forms.
OEIS A301429 Decimal expansion of an analog of the Landau-Ramanujan constant for Loeschian numbers.
OEIS A301430 Decimal expansion of an analog of the Landau-Ramanujan constant for Loeschian numbers which are sums of two squares.
Integer--valued functions, Hurwitz functions and related topics: a survey.
27 pages. To appear in the proceedings of the 2019 Journées Arithmétiques (Istanbul).
arXiv:2002.01223 [math.NT]
Third kind elliptic integrals and transcendance (3 pages). Appendix to the paper
Third kind elliptic integrals and 1-motives by Cristiana Bertolin.
Journal of Pure and Applied Algebra,
Volume 224, Issue 10, October 2020, 106396, 1-28.
DOI 10.1016/j.jpaa.2020.106396
arXiv:1905.07247 [math.NT]
Thue Diophantine equations - a survey.
Class Groups of Number Fields and Related Topics, ed. Kalyan Chakraborty, Azizul Hoque and Prem Prakash Pandey, p. 25-41 . Springer Nature Singapore Pte Ltd., 2020.
Proceedings of the International Conference ICCGNFRT-2017, HRI Allahabad, September 2017.
DOI 10.1007/978-981-15-1514-9_3
Les fichiers pdf ou ppt de mes exposés
récents ou
plus anciens sont téléchargeables.
You can download the pdf or ppt files of my
recent or
not so recent lectures and talks.
In English
Transcendental Number Theory: recent results and open problems.
pdf file 5.7 Mo, 99p.
update 2021
Schanuel's Conjecture: algebraic independence of transcendental numbers.
pdf file 21.5 Mo, 68 p.
update 2021
Irrationality and transcendence of values of special functions.
pdf 11.2 Mo, 112p.
update 2021
Online course CIMPA on Interpolation.
pdf files:
course 1, 1.6 Mo, 48 pages,
course 2, 406 Ko, 49 pages,
course 3, 934 Ko, 50 pages,
course 4, 1.6 Mo, 65 pages.
Link to the videos on You Tube (December 2020)
Exercices
Sheet 1,
Corrections.
Sheet 2,
Corrections.
Sheet 3,
Corrections.
Sheet 4,
Corrections.
update 2021
Some variants of Seshadri's constant.
slides pdf 14.4 Mo, 104p.
Link to the video (October 12, 2020).
update 2020
An introduction to the theory of finite fields (pdf: 82 pages).
update 2020
Linear recurrence sequences.
Part I, examples.
Link to the video, September 21, 2020.
Part II, the theory.
Link to the video, September 28, 2020.
update 2020
On the Brahmagupta-Fermat-Pell Equation.
print pdf: 2.3 Mo, 86 p.
The video
(July 23, 2020) is available on You Tube.
update 2020
The square root of 2, the Golden ratio and the Fibonacci sequence.
print pdf 4.5 Mo, 89p.
The video (July 20, 2020) is available on
YouTube
update 2020
Srinivasa Ramanujan His life and his work.
pdf slides, Link to a video (December 16, 2020).
Link to another video on You Tube (Dec. 29, 2020).
update 2020
Integer valued entire functions.
screen pdf 2.3 Mo, 171p.
print pdf 1.1 Mo, 17p.
see also the
Online course CIMPA on Interpolation.
pdf file:
course 4, 1.6 Mo, 65 pages.
Link to the video on You Tube (December 15, 2020).
update 2020
Lidstone series, generalisations and arithmetic applications.
screen pdf 764 Ko, 131p.
print pdf 792 Ko, 15p.
see also the
Online course CIMPA on Interpolation.
pdf files:
course 2, 406 Ko, 49 pages,
course 3, 934 Ko, 50 pages,
Link to the videos on You Tube (Dec. 2020)
update 2020
Representation of integers by cyclotomic binary forms.
43p., 3.6 Mo.
Number Theory Web Seminar,
Tuesday, May 12, 2020.
Link to recording and slides
update 2020
Introduction to Galois Theory
screen pdf: 4,2 Mo, 85 p.
print pdf: 1,1 Mo, 15 p.
update 2019
Some of the most famous open problems in number theory.
screen pdf: 5.8 Mo, 214 p.
print pdf: 1.8 Mo, 28 p.
update 2019
Continued fractions: introduction and applications.
screen pdf: 3.7 Mo, 147 p.
print pdf: 1.1 Mo, 20 p.
update 2019
See also
Continued fractions (unpublished manuscript, 46 pages).
The unity of mathematics - examples from transcendental number theory.
pdf file, screen version: 4.1 Mo, 147p.
pdf file, print version: 1.4 Mo, 20p.
Video on YouTube of the
first and
third courses (October 2018).
update 2018
On the Landau--Ramanujan constant
pdf file, screen version: 3.4 Mo, 130 p.
pdf file, print version: 1.1 Mo, 18 p.
update 2018
An elementary introduction to error correcting codes.
powerpoint file (161 p., 4.3 Mo)
pdf file (44 p., 5.5 Mo).
update 2018
An elementary introduction to cryptography.
powerpoint file (95 p., 3.6 Mo)
pdf file (24 p., 6.2 Mo).
update 2018
Is the Euler constant a rational number, an algebraic irrational number or else a transcendental number?
pdf file, screen version: 3.4 Mo, 126 p.
pdf file, print version: 1.3 Mo, 22 p.
update 2017
On the abc conjecture and some of its consequences.
screen pdf: 5.5 Mo, 195 p.
print pdf: 2.1 Mo, 30 p.
update 2017
On the Markoff equation x^2+y^2+z^2=3xyz;
screen pdf 4.6 Mo, 171 p.
print pdf 4.8 Mo, 22 p.
update 2016
Diophantine equations and Diophantine approximations
screen pdf: 3.2 Mo, 161 p.
print pdf: 1.9 Mo, 23 p.
update 2016
See also
Families of Diophantine equations.
screen pdf 1.9 Mo, 99p.
print pdf 1.3 Mo, 15p.
update 2016
Diophantine approximation with applications to dynamical systems.
screen pdf: 1.2 Mo, 119 p.
print pdf: 1.2 Mo, 14 p.
update 2016
Multiple zeta values.
screen pdf: 2.3 Mo, 151 p.
print pdf: 2.3 Mo, 19 p.
update 2014
Diophantine equations and Diophantine approximation
screen pdf: 1.3 Mo, 96 p.
print pdf: 1.3 Mo, 16 p.
update 2012
En français
Le Podcast de la culture mathématique: Trajectoires #18: Nombres Transcendants (23 september 2019).
Les débuts de la théorie des nombres transcendants.
fichier pdf, version écran: 4,2 Mo, 52 pages
fichier pdf, version à imprimer: 3,2 Mo, 11 pages
mise à jour 2019
Introduction à la cryptographie.
fichier powerpoint, 3,4 Mo, 89 pages
fichier pdf, version à imprimer, 6,2 Mo, 23 pages.
mise à jour 2018
introduction aux codes correcteurs d’erreurs
fichier ppt, 4 Mo, 164 p.
fichier pdf, version à imprimer:
5,9 Mo, 41p.
mise à jour 2018
L'équation de Brahmagupta - Pell - Fermat.
fichier pdf, version écran: 3,3 Mo, 193 p.
fichier pdf, version à imprimer: 3,3 Mo, 21 p.
mise à jour 2017
Sur l’équation de Markoff x^2+y^2+z^2=3xyz.
fichier pdf, version écran 4,9 Mo, 221 p.
fichier pdf, version à imprimer 5 Mo, 27 p.
mise à jour 2016
La conjecture abc
fichier pdf, version écran 19,4 Mo, 152 p.
fichier pdf, version à imprimer 19,6 Mo, 25 p.
mise à jour 2016
Fractions continues, introduction et applications
fichier pdf, version écran: 3,7 Mo, 145 p.
fichier pdf, version à imprimer: 3,7 Mo, 20 p.
mise à jour 2016
Problèmes ouverts en théorie des nombres.
fichier pdf, version écran: 4,4 Mo, 203 p.
fichier pdf, version à imprimer: 4,4 Mo, 27 p.
mise à jour 2015
La constante d'Euler est-elle un nombre rationnel, un nombre algébrique irrationnel ou bien un nombre transcendant?
fichier pdf, version écran: 4,5 Mo, 128 p.
fichier pdf, version à imprimer: 4,5 Mo, 22 p.
mise à jour 2014
Nombres transcendants: résultats récents et problèmes ouverts
fichier pdf, version écran 4,4 Mo, 142 p.
fichier pdf, version à imprimer 3,9 Mo, 15 p.
mise à jour 2009
Valeurs zêta multiples, d'Euler à nos jours.
fichier pdf, version écran 2,2 Mo, 236 p.
fichier pdf, version à imprimer 1,1 Mo, 26 p.
mise à jour 2008