Abstract: The "poor man's adèle ring" is the ring of sequences of integers modulo p. Kaneko and Zagier introduced this terminology to study families of mod p congruences of multiple harmonic sums, discovering that these congruences have “real” counterparts in their main conjecture. In this talk, we address the question of whether, for a given element $x$ in the poor man's adèle ring, we can find a $P$-recursive sequence$(a_n{)}_n$such that $x=(a_{p}modp{)}_p$​. We present examples of such elements derived from Bernoulli numbers and weight 1 modular forms. Additionally, we will discuss Apéry limits within the context of the poor man's adèle ring.

 

Organizer: Nobuo Sato (NTU)