Congruences for the Ramanujan function and generalized class numbers
نویسنده
چکیده
The Ramanujan τ -function satisfies well-known congruences modulo the so-called exceptional prime numbers 2, 3, 5, 7, 23, 691. In this paper we prove new congruences related to the irregular primes 131 and 593, involving generalized class numbers. As an application we obtain distribution results. We obtain a new proof of the famous 691 congruence and congruences of the related Rankin L-funtion.
منابع مشابه
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Ramanujan-type congruences for the unrestricted partition function p(n) are well known and have been studied in great detail. The existence of Ramanujan-type congruences are virtually unknown for p(n,m), the closely related restricted partition function that enumerates the number of partitions of n into exactly m parts. Let ` be any odd prime. In this paper we establish explicit Ramanujan-type ...
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ورودعنوان ژورنال:
- Math. Comput.
دوره 78 شماره
صفحات -
تاریخ انتشار 2009