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Simple Calculation of the Residues of the Adelic Zeta Function Associated with the Space of Binary Cubic Forms

✍ Scribed by T. Kogiso

Publisher: Elsevier Science
Year: 1995
Tongue: English
Weight: 359 KB
Volume: 51
Category: Article
ISSN: 0022-314X
DOI: 10.1006/jnth.1995.1045

No coin nor oath required. For personal study only.

✦ Synopsis

In this note, we calculate the residues of an adelic zeta function associated with the space of binary cubic forms over any number field without using Eisenstein series. 1995 Academic Press. Inc.

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## Abstract Let __N__ ∈ ℕ and let __χ__ be a Dirichlet character modulo __N__. Let __f__ be a modular form with respect to the group Γ~0~(__N__), multiplier __χ__ and weight __k__. Let __F__ be the __L__ ‐function associated with __f__ and normalized in such a way that __F__ (__s__) satisfies a fun