$p$-adic $L$-functions and classical congruences
Volume 194 / 2020
Acta Arithmetica 194 (2020), 29-49
MSC: Primary 11A07; Secondary 11B68, 11B65, 11S40.
DOI: 10.4064/aa181207-2-5
Published online: 21 February 2020
Abstract
Using $p$-adic analysis and $p$-adic $L$-functions, we show how to extend classical congruences (due to Wilson, Gauss, Dirichlet, Jacobi, Wolstenholme, Glaisher, Morley, Lehmer and other people) to modulus $p^k$ for any $k \gt 0$.
