Variations of Ramanujan's Euler Products
Shin-ya Koyama, Nobushige Kurokawa
TL;DR
This paper investigates the meromorphic properties of degree-two Euler products linked to cusp forms, including Ramanujan's Delta function, expanding understanding of their analytic behavior.
Contribution
It provides new insights into the meromorphic nature of Euler products associated with cusp forms, particularly focusing on Ramanujan's Delta function.
Findings
Identifies conditions for meromorphy of degree-two Euler products.
Analyzes the specific case of Ramanujan's Delta function.
Contributes to the theory of automorphic L-functions.
Abstract
We study the meromorphy of various Euler products of degree two attached to cusp forms including Ramanujan's -function.
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Taxonomy
TopicsAdvanced Mathematical Identities · Advanced Algebra and Geometry · Analytic Number Theory Research