68 citations · 113 across the 19 of their papers we have counts for
19 papers
A supercongruence fantasy on Fibonacci and Lucas (after Guillera)
Wadim Zudilin
Motivated by observations of Guillera we generalise the so-called Ramanujan-type supercongruences to a further level in which the sequences of Fibonacci, Lucas, Apéry numbers and t…
Galois Groups of Apéry-like Series Modulo Primes
Xavier Caruso, Florian Fürnsinn, Daniel Vargas-Montoya +1
We compute the Galois groups of the reductions modulo the prime numbers of the generating series of Apéry numbers, Domb numbers and Almkvist--Zudilin numbers. We observe in par…
Continued Fractions and Irrationality Measures for Chowla--Selberg Gamma Quotients
Henri Cohen, Wadim Zudilin
We give 39 rapidly convergent continued fractions for Chowla--Selberg gamma quotients, and deduce good irrationality measures for 20 of them, including for $\operatorname{CS}(-3)=(…
Linear independence measures for Chowla--Selberg periods
Wadim Zudilin
We use simultaneous Padé approximations to hypergeometric functions to estimate from below linear forms in , , and with integral coefficients,…
Poor man's transcendence for Frobenius traces of elliptic curves
Florian Luca, Wadim Zudilin
Let be an elliptic curve without complex multiplication defined over . Viewing the sequence of its Frobenius traces indexed by primes as an element…
Irrationality and transcendence questions in the "poor man's adèle ring"
Florian Luca, Wadim Zudilin
We discuss arithmetic questions related to the "poor man's adèle ring" whose elements are encoded by sequences indexed by prime numbers, with each view…
-rious unimodality
S. Ole Warnaar, Wadim Zudilin
We generalise our still-wide-open -rious positivity conjecture from 2011 to a -rious unimodality conjecture.
Variations on a theme of Apéry
Henri Cohen, Wadim Zudilin
Apéry's remarkable discovery of rapidly converging continued fractions with small coefficients for and has led to a flurry of important activity in an incredible vari…
First memoir on the asymptotics of certain infinite products
Wadim Zudilin
The product sides of the Rogers--Ramanujan identities and alike often appear to be "transparently modular" (functions). The old work by Rogers (1894) and recent work by Rosengren m…
An evolution of matrix-valued orthogonal polynomials
Erik Koelink, Pablo Román, Wadim Zudilin
We establish new explicit connections between classical (scalar) and matrix Gegenbauer polynomials, which result in new symmetries of the latter and further give access to several…
A BBP-style computation for in base 5
Wadim Zudilin
We joke about how to compute (promptly) the digits of , in base 5, from a given place without computing preceding ones.
A partial-sum deformation for a family of orthogonal polynomials
Erik Koelink, Pablo Román, Wadim Zudilin
There are several questions one may ask about polynomials attached to a family of orthogonal polynomials . In this note…
A non-ordinary (prime) note
Wadim Zudilin
Given a newform with the Fourier expansion , a prime is said to be non-ordinary if . We exemplify several newforms of we…
Continued fractions of cubic irrationalities
Wadim Zudilin
We highlight some facts about continued fractions of real cubic irrationalities. This may be thought as a small section in a textbook on continued fractions.
Hedgehogs in Lehmer's problem
Jan-Willem M. van Ittersum, Berend Ringeling, Wadim Zudilin
Motivated by a famous question of Lehmer about the Mahler measure we study and solve its analytic analogue.
A case study for
Carsten Schneider, Wadim Zudilin
Using symbolic summation tools in the setting of difference rings, we prove a two-parametric identity that relates rational approximations to .
Densities of short uniform random walks
Jonathan M. Borwein, Armin Straub, James Wan +1
We study the densities of uniform random walks in the plane. A special focus is on the case of short walks with three or four steps and less completely those with five steps. As on…
Experimental Mathematics and Mathematical Physics
David H. Bailey, Jonathan M. Borwein, David Broadhurst +1
One of the most effective techniques of experimental mathematics is to compute mathematical entities such as integrals, series or limits to high precision, then attempt to recogniz…
A q-rious positivity
S. Ole Warnaar, Wadim Zudilin
The -binomial coefficients $\qbinom{n}{m}=\prod_{i=1}^m(1-q^{n-m+i})/(1-q^i)$, for integers , are known to be polynomials with non-negative integer coefficients. Th…