Introduction to Applications of Modular Forms: Computational Aspects by Zafer Selcuk Aygin

Author:Zafer Selcuk Aygin
Language: eng
Format: epub
ISBN: 9783031326295
Publisher: Springer International Publishing

Now finding the Eisenstein part of for each R and is a straightforward application of Theorem 2.​6.​1. Next, we illustrate this by discussing the cases when where p is a prime congruent to 3 modulo 4. We note that the following result goes back to Dirichlet (when n and p are coprime), see [28, p. 78], and see [33, Theorem 9.1] for an elementary proof (including the cases when n and p are not coprime).

Theorem 3.3.2

Let where p is a prime congruent to 3 modulo 4. Then for all divisors of R we have

(3.2)

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