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arXiv · 2508.07478

A note on arithmetic congruences

Nic Fellini
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Abstract

By analyzing the coefficients of the power series defining the Kubota--Leopoldt $p$-adic $L$-function associated to the non-trivial character of a real quadratic field, we prove a congruence of Ankeny--Artin--Chowla-type for prime power modulus. Additionally, we show how some classical congruences relating Bernoulli numbers and Wilson quotients fit naturally into the theory of the $p$-adic Riemann zeta function.

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Nic Fellini. 2025-08-10. A note on arithmetic congruences. https://arxiv.org/abs/2508.07478

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