منابع مشابه
Euler Products and Twisted Euler Products
We describe in brief some aspects of the Langlands program, focussing on Euler products, and also some new constructions, where Euler products are replaced by twisted Euler products. The twisted Euler products are related to automorphic forms on metaplectic groups. 2000 Mathematics Subject Classification: 11F66, 11F55, 11F70, 11M41, 22E55.
متن کاملZero distributions for meromorphic Euler products
The aim of the present paper is to study distributions of singular points of a zeta function which is expressed by an Euler product and is analytically continued as a meromorphic function of finite order. In this manuscript, we give a relation between the growth of the multiplicities for the norms of primitive elements and the order of the zeta function as a meromorphic function.
متن کاملEuler Products in Ramanujan’s Lost Notebook
In his famous paper, “On certain arithmetical functions”, Ramanujan offers for the first time the Euler product of the Dirichlet series in which the coefficients are given by Ramanujan’s tau-function. In his lost notebook, Ramanujan records further Euler products for L-series attached to modular forms, and, typically, does not record proofs for these claims. In this semi-expository article, for...
متن کاملPartial Euler Products on the Critical Line
The initial version of the Birch and Swinnerton-Dyer conjecture concerned asymptotics for partial Euler products for an elliptic curve L-function at s = 1. Goldfeld later proved that these asymptotics imply the Riemann hypothesis for the L-function and that the constant in the asymptotics has an unexpected factor of √ 2. We extend Goldfeld’s theorem to an analysis of partial Euler products for ...
متن کاملFix-euler-mahonian Statistics on Wreath Products
In 1997 Clarke, Han, and Zeng introduced a q-analogue of Euler’s difference table for n! using a key bijection Ψ on symmetric groups. In this paper we extend their results to the wreath product of a cyclic group with the symmetric group. By generalizing their bijection Ψ we prove the equidistribution of the triple statistics (fix, exc, fmaj) and (fix, exc, fmaf) on wreath products, where “fix”,...
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ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 2006
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa121-1-3