Dessin par Hélène
Michel Waldschmidt

EMS Newsletter March 2019
    Interview by Ulf Persson published in the Newsletter of the European Mathematical Society, March 2019, issue 111, p. 23-26.

Le Podcast de la culture mathématique: Trajectoires #18: Nombres Transcendants.

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.

Agenda

Archives from January 2009 till now.

Prochaînement - Coming soon

December 7-10, CIMPA, Nice.
    Recording the courses for the course on Interpolation formulae (see Mumbai Ramnarain Ruia Autonomous College, January 4-8, 2021).

December 11 - 14, 2020, Cochin (India) Web conference using Google Meet
    International Conference on Number theory and Discrete Mathematics. Organized by the Ramanujan Mathematical Society. Rajagiri School of Engineering & Technology.

January 4-8, 2021. Mumbai (India) Online.
    Mumbai Ramnarain Ruia Autonomous College, under the GIAN scheme of MHRD, UM-DAE Centre for Excellence in Basic Sciences (CEBS). A course on Interpolation formulae.

January 6-9, 2021. The 2021 Joint Mathematics Meetings (JMM) will take place virtually.

25 janvier - 4 février 2021. Limbe (Cameroun)
    Cours de théorie analytique des nombres à African Institute for Mathematical Sciences (AIMS) Cameroun.

April 12 - 23,2021: Hanoi (Vietnam)
    CIMPA School on Functional Equations: Theory, Practice and Interaction. Course: Introduction to transcendental number theory.

May 10-15, 2021, Marina di San Gregorio, Patù (Lecce), Italy
    Leuca2021 Celebrating Claude Levesque's and Michel Waldschmidt's 75th birthdays.

June 28 - July 2, 2021. M'Bour, Senegal
    CIMPA School on cryptography, theoretical and computational aspects of number theory. Course: Elementary approach to elliptic curves. African Institute for Mathematical Sciences (AIMS) Senegal. The school is June 28 - July 9, 2021.

July 5 - 9, 2021: Nancy.
    Journées arithmétiques 2021.

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 will be July 26 - August 6.

(?) 2021 Port Moresby, Papua New Guinea. (Initially planned December 7 - 11, 2020)
    The Third International Conference on Pure and Applied Mathematics ICPAM3, Pacific Adventist University. "Mathematical Contributions to the building of a Healthy, Wealthy, Wise, Smart, Fair and Happy Nation."

Research paper (to appear) - Article de recherche (à paraitre)

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. 21 pages. Moscow Journal of Combinatorics and Number Theory, to appear.
    arXiv: 1912.00174 [math.NT].

Research papers (recently published) - Articles de recherche (viennent de paraître)

Avec Etienne Fouvry,
    Sur la représentation des entiers par des formes cyclotomiques de grand degré. Bulletin de la Société Mathématique de France, tome 148 fascicule 2, 253-282.

With Etienne Fouvry and Claude Levesque,
    Representation of integers by cyclotomic binary forms. Acta Arithmetica, 184.1 (2018), 67 - 86. Online First March 2018.
    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.

Recent surveys - articles de synthèse récents

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.

With Razvan Barbulescu. Poster summarizing The abc conjecture and some of its consequences. Archives HAL.

Lectures - Courses - Conferences - Videos

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

Some variants of Seshadri's constant. slides pdf 14.4 Mo, 104p. Link to the video, New York Online Number Theory Colloquium, October 12, 2020.

An introduction to the theory of finite fields (pdf: 82 pages). 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

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.
        update 2020
        The video of the International Web Conference on "Mathematics for Signals, Images, and Structured Data" - ICMMSIS'20, (July 23, 2020) is available on You Tube.

The square root of 2, the Golden ratio and the Fibonacci sequence.     print pdf 4.5 Mo, 89p.
        The video of the lecture I gave for the Kurdish Mathematics School on July 20, 2020 is available on YouTube

Integer valued entire functions.     screen pdf 2.3 Mo, 171p.     print pdf 1.1 Mo, 17p.
        update 2019

Lidstone series, generalisations and arithmetic applications.
        screen pdf 764 Ko, 131p.   print pdf 792 Ko, 15p.
        update 2019

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.
        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

Transcendental Number Theory: recent results and open problems.
        screen pdf 3.3 Mo, 193p.   print pdf 1.7 Mo, 24p.
        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

Irrationality and transcendence of values of special functions.
        screen pdf 10.6 Mo, 185p.   print pdf 9.3 Mo, 25p.
        update 2016

Two invariants related to two conjectures due to Nagata.
        screen pdf 10.4 Mo, 170p.   print pdf 10.4 Mo, 26p.
        update 2019

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

Schanuel's Conjecture: algebraic independence of transcendental numbers.
        screen pdf: 21.7 Mo, 127 p.   print pdf: 21.7 Mo, 17 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

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