13 papers
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)=(…
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…
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…
-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 v…
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 pa…