A series of new congruences for Bernoulli numbers and Eisenstein series

[摘要] We prove congruences of shape Ek+h = E-k . E-h (mod N) modulo powers N of small prime numbers p, thereby refining the well-known Kummer-type congruences modulo these p of the normalized Eisenstein series E-k. The method uses Serre's theory of Iwasawa functions and p-adic Eisenstein series; it presents a rather general procedure to find and verify such congruences with a modest amount of numerical calculation. (C) 2002 Elsevier Science (USA).

[发布日期] 2002-11-01