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Congruences for the Ramanujan function and generalized class numbers
Author(s):
Bernhard
Heim.
Journal:
Math. Comp.
MSC (2000):
Primary 11F33, 11F67, 11F80;
Secondary 11Y70
Posted:
May 20, 2008
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Abstract:
The Ramanujan  -function satisfies well-known congruences modulo the so-called exceptional prime numbers  . In this paper we prove new congruences related to the irregular primes  and  , involving generalized class numbers. As an application we obtain distribution results. We obtain a new proof of the famous  congruence and congruences of the related Rankin L-funtion.
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MR 0485703 (58:5525)
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Additional Information:
Bernhard
Heim
Affiliation:
Max-Planck Institut für Mathematik, Vivatsgasse 7, 53111 Bonn, Germany
Email:
heim@mpim-bonn.mpg.de
DOI:
10.1090/S0025-5718-08-02136-4
PII:
S 0025-5718(08)02136-4
Received by editor(s):
November 13, 2007
Received by editor(s) in revised form:
January 9, 2008
Posted:
May 20, 2008
Copyright of article:
Copyright
2008,
American Mathematical Society
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