Analytic behavior of some Euler products

2021 ◽  
Vol 51 (2) ◽  
Author(s):  
Jinho Han ◽  
Haseo Ki ◽  
Donghoon Park
Keyword(s):  
Analytic Behavior ◽  
Euler Products

scholarly journals Natural boundaries for Euler products of Igusa zeta functions of elliptic curves

2018 ◽  
Vol 14 (08) ◽  
pp. 2317-2331
Author(s):  
Marcus du Sautoy
Keyword(s):  
Elliptic Curves ◽  
Zeta Functions ◽  
Symmetric Power ◽  
Meromorphic Continuation ◽  
Natural Boundary ◽  
Integer Polynomials ◽  
Analytic Behavior ◽  
Euler Products ◽  
Natural Boundaries

We study the analytic behavior of adelic versions of Igusa integrals given by integer polynomials defining elliptic curves. By applying results on the meromorphic continuation of symmetric power L-functions and the Sato–Tate conjectures, we prove that these global Igusa zeta functions have some meromorphic continuation until a natural boundary beyond which no continuation is possible.

Effective Estimates for the Distribution of Values of Euler Products

2005 ◽  
Vol 145 (2) ◽  
pp. 97-106 ◽  
Author(s):  
Ernesto Girondo ◽  
Jörn Steuding
Keyword(s):  
Distribution Of Values ◽  
Euler Products

scholarly journals Ramanujan identities and Euler products for a type of Dirichlet series

2006 ◽  
Vol 122 (4) ◽  
pp. 349-393 ◽  
Author(s):  
Zhi-Hong Sun ◽  
Kenneth S. Williams
Keyword(s):  
Dirichlet Series ◽  
Euler Products

scholarly journals On an identity of Ramanujan

2019 ◽  
Author(s):  
Yoichi Motohashi
Keyword(s):  
Original Proof ◽  
International Audience ◽  
Euler Products ◽  
Ramanujan Identity

International audience Proofs published so far in articles and books, of the Ramanujan identity presented in this note, which depend on Euler products, are essentially the same as Ramanujan's original proof. In contrast, the proof given here is short and independent of the use of Euler products.

scholarly journals On certain Euler products

1987 ◽  
Vol 48 (1) ◽  
pp. 49-52 ◽  
Author(s):  
N. Kurokawa
Keyword(s):  
Euler Products
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