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$p$-adic $L$-functions and classical congruences

Volume 194 / 2020

Xianzu Lin Acta Arithmetica 194 (2020), 29-49 MSC: Primary 11A07; Secondary 11B68, 11B65, 11S40. DOI: 10.4064/aa181207-2-5 Published online: 21 February 2020


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 $k \gt 0$.


  • Xianzu LinCollege of Mathematics and Informatics
    Fujian Normal University
    Fuzhou, 350108, China

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