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Eisenstein series and Ramanujan-type series for 1/π

✍ Scribed by Nayandeep Deka Baruah; Bruce C. Berndt

Publisher
Springer US
Year
2009
Tongue
English
Weight
592 KB
Volume
23
Category
Article
ISSN
1382-4090

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A Series of New Congruences for Bernoull
A Series of New Congruences for Bernoulli Numbers and Eisenstein Series
✍ Ernst-Ulrich Gekeler 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 133 KB

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 presen