We study properties of coefficients of a linear form, originating from a multiple integral. As a corollary, we prove Vasilyev's conjecture, connected with the problem of irrationality of the Riemann zeta function at odd integers.

Apéry’s proof [13] of the irrationality of ζ(3) is now over 25 years old, and it is perhaps surprising that his methods have not yielded any significant new results (although further progress has been made on the irrationality of zeta values [1, 14]). Shortly after the initial proof, Beukers produced two elegant reinterpretations of Apéry’s arguments; the first using iterated integrals and Lege...

Apéry’s proof [11] of the irrationality of ζ(3) is now over 25 years old, and it is perhaps surprising that his methods have not yielded any significantly new results (although further progress has been made on the irrationality of zeta values [1], [12]). Shortly after the initial proof, Beukers produced two elegant reinterpretations of Apéry’s arguments; the first using iterated integrals and ...

It is widely agreed that obsessive-compulsive disorder involves irrationality. But where in the complex of states and processes constitutes OCD should this irrationality be located? A pervasive assumption both psychiatric philosophical literature seat located obsessive thoughts characteristic OCD. Building on a puzzle about insight into OCD, we challenge assumption, argue instead emotions are s...

The three main methods used in diophantine analysis of q-series are combined to obtain new upper bounds for irrationality measures of the values of the q-logarithm function