Wadim Zudilin

I am Professor of Pure Mathematics at the Radboud University Nijmegen, Faculty of Science.

w [dot] zudilin [at] math [dot] ru [dot] nl;
wzudilin [at] gmail [dot] com

Wadim Zudilin
Institute for Mathematics, Astrophysics and Particle Physics
Radboud Universiteit, PO Box 9010
6500 GL Nijmegen, Netherlands

orcid.org/0000-0001-9551-2903

Research interests (though listed below in obscure alphabetical order, all items are considered by me as pieces of a single whole)
- Apéry's theorem
- Calabi–Yau differential equations
- Continued fractions
- Dilogarithm
- Diophantine approximations
- Diophantine equations
- Elliptic curves
- Elliptic functions
- Experimental Mathematics
- Hankel determinants
- Hypergeometric functions
- Hypergeometric motives
- Irrationality and transcendence
- L-values
- Mahler measures
- Mahler functions
- Mathematical constants
- Mock theta functions
- Modular forms and functions
- Multiple zeta values
- Number Theory in general
- Ordinary zeta values
- Orthogonal polynomials
- Padé approximations
- π
- Positivity
- Ramanujan's mathematics
- Rogers–Ramanujan identities
- Special functions
- Supercongruences and their q-analogues
PhD thesis
- "On the estimates of the measure of linear independence for values of certain analytical functions" (in Russian), also in html format
  Moscow State University, 1 December 1995
Habilitation (D.Sc. thesis)
- "Apéry's theorem and problems for the values of Riemann's zeta function and their q-analogues" (in Russian),
  Moscow State University, 20 June 2014
Books
- Just appeared in print: Analytic Methods in Number Theory: When Complex Numbers Count (World Scientific, 2023)
- Many Variations of Mahler Measures: A Lasting Symphony (Cambridge University Press, 2020),
  with François Brunault
- Neverending Fractions: An Introduction to Continued Fractions (Cambridge University Press, 2014),
  with Jonathan Borwein, Alf van der Poorten and Jeffrey Shallit
Interviews
- Interview with Ali Kemal Uncu (Strobl, 8 September 2020)
Books & papers (check also my list of publications in Mathematical Reviews, Zentralblatt, Google Scholar and arXiv)
Collaborators
Talks & activities
Editorial duties
- Integral Transforms and Special Functions, Member of the Editorial Board (2013– )
- Journal of Algebraic Combinatorics, Associate Editor (2018– )
- Results in Mathematics, Associate Editor (2023– )
- Monographs in Number Theory, Editor (2008–2013) & Series Editor (2013– )
- NIST Digital Library of Mathematical Functions, Associate Editor for the Chapter on Zeta and Related Functions (2015– )
- formerly The Ramanujan Journal, Coordinating Editor (2018–2021)
- formerly International Journal of Number Theory, Associate Editor (2009–2011 & 2014–2020)
- formerly Bulletin of the Australian Mathematical Society, Associate Editor (2013–2017)
- formerly Journal of the Australian Mathematical Society, Associate Editor (2013–2017)
Awards
- Distinguished Award of the Hardy–Ramanujan Society (2001)
- Our joint paper Densities of short uniform random walks (with an appendix by D. Zagier),
  with Jonathan Borwein, Armin Straub and James Wan,
  has been awarded the 2014 G. de B. Robinson Award of the Canadian Mathematical Society
PhD students
- Jesús Guillera Goyanes, "Series de Ramanujan: Generalizaciones y conjeturas" ("Ramanujan's series: Generalizations and conjectures"),
  Facultad de Ciencias, Departamento de Matemáticas, Universidad de Zaragoza (Zaragoza, Spain, 2 July 2007)
- Igor P. Rochev, "Arithmetic properties of values of certain analytic functions",
  Department of Mechanics and Mathematics, Moscow Lomonosov State University (Moscow, Russia, 18 February 2011)
- Yuri A. Pupyrev, "Arithmetic applications of the theory of hypergeometric series",
  Department of Mechanics and Mathematics, Moscow Lomonosov State University (Moscow, Russia, 18 February 2011)
- James Wan, "Random walks, elliptic integrals, and related constants",
  School of Mathematical and Physical Sciences, The University of Newcastle (Newcastle, NSW, Australia, 19 March 2013)
- Daniel Sutherland, "Arithmetic applications of Hankel determinants",
  School of Mathematical and Physical Sciences, The University of Newcastle (Newcastle, NSW, Australia, 13 February 2015)
- Berend Ringeling, "Mahler measures, modular forms and hypergeometric functions",
  Institute for Mathematics, Astrophysics and Particle Physics, Radboud University (Nijmegen, Netherlands, 23 October 2023)
(Under)graduate supervision
- Alexander Dunn, "Nahm's conjecture in the Cartan case" (pdf),
  MPhil thesis (University of Queensland, QLD, Australia, 2015)
- Milutin Branković, "Lehmer's problem and the Newton polygon" (pdf),
  BSc honours thesis (University of Newcastle, NSW, Australia, June 2016)
- Boaz Moerman, "Eisenstein series and periods",
  published as "L-values for conductor 32" (arXiv, ),
  BSc honours thesis (Radboud University Nijmegen, Netherlands, June 2019)
- Abel Vleeshouwers, "Multiple zeta values and their q-analogues" (arXiv),
  MSc thesis (Radboud University Nijmegen, Netherlands, July 2020)
- Joris Nieuwveld, "Fractions, functions and folding. A novel link between continued fractions, Mahler functions and paper folding" (arXiv & my summary),
  MSc thesis (Radboud University Nijmegen, Netherlands, August 2021)
- Björn Johannesson, "Sequences related to Lehmer's problem" (arXiv),
  MSc thesis (Radboud University Nijmegen, Netherlands, June 2023)
My favourite constants
- π = 3.14159265358979323846264338327950288419716939937510...
- Pi down under 1/π = 0.31830988618379067153776752674502872406891929148091...
- π²/6 = ζ(2) = 1.64493406684822643647241516664602518921894990120679...
- Apéry's constant ζ(3) = 1.20205690315959428539973816151144999076498629234049...
- ζ(5) = 1.03692775514336992633136548645703416805708091950191...
- Catalan's constant G = 0.91596559417721901505460351493238411077414937428167...
- Euler's constant γ = 0.57721566490153286060651209008240243104215933593992...
Other resources on my web
- Zeta values on the Web is a collection of references and links devoted to the arithmetic study of values of the Riemann zeta function at positive integers and related constants (abandoned)
- Catalan's problem has been solved successfully by P. Mihailescu; here are some theorems and links related to the problem
- Some arts by my son Victor
- "Diophantine Approximations", Mathematical Transactions 2 (1996) Collection of papers dedicated to memory of Prof. N.I. Feldman (Russian)
- "Analytic Number Theory and Applications", Proc. V.A. Steklov Inst. Math. 218 (1997) Collection of papers. To Prof. Anatolii Alexeevich Karatsuba on occasion of his 60th birthday (Russian & English)

Started on July 2, 1997