R. Osburn

activity

20042023

most citedA p-adic analogue of a formula of Ramanujan

77 citations · 784 across the 49 of their papers we have counts for

collaborators

Showing 2017 · math.NTShow all

3 papers · 2 filters

math.NT2017★ 2 cited

Constrained ternary integers

Florian Luca, Pieter Moree, Robert Osburn +2

An integer $n$ is said to be ternary if it is composed of three distinct odd primes. In this paper, we asymptotically count the number of ternary integers $n \leq x$ with the const…

math.NT2017★ 9 cited

Sequences, modular forms and cellular integrals

Dermot McCarthy, Robert Osburn, Armin Straub

It is well-known that the Apéry sequences which arise in the irrationality proofs for $ζ (2)$ and $ζ (3)$ satisfy many intriguing arithmetic properties and are related to the $p$ th F…

math.NT2017★ 20 cited

A modular supercongruence for $_{6} F_{5}$ : an Apéry-like story

Robert Osburn, Armin Straub, Wadim Zudilin

We prove a supercongruence modulo $p^{3}$ between the $p$ th Fourier coefficient of a weight 6 modular form and a truncated $_{6} F_{5}$ -hypergeometric series. Novel ingredients in the p…

Constrained ternary integers

Sequences, modular forms and cellular integrals

A modular supercongruence for 6​F5​: an Apéry-like story

A modular supercongruence for $_{6} F_{5}$ : an Apéry-like story