A Series of New Congruences for Bernoulli Numbers and Eisenstein Series

✍ Scribed by Ernst-Ulrich Gekeler

• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 133 KB
• Volume: 97
• Category: Article
• ISSN: 0022-314X
• DOI: 10.1006/jnth.2002.2802

✦ Synopsis

We prove congruences of shape E kþh E k Á E h ðmod NÞ 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. # 2002 Elsevier Science (USA)