The Selberg Class

2001 ◽  
pp. 115-126
Author(s):  
M. Ram Murty
Keyword(s):  
Selberg Class

scholarly journals On the structure of the Selberg class, IV: basic invariants

2002 ◽  
Vol 104 (2) ◽  
pp. 97-116 ◽  
Author(s):  
J. Kaczorowski ◽  
A. Perelli
Keyword(s):  
Selberg Class ◽  
Class Iv

scholarly journals Uniqueness of L-Functions Concerning Certain Differential Polynomials

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Wen-Jie Hao ◽  
Jun-Fan Chen
Keyword(s):  
Nevanlinna Theory ◽  
Selberg Class ◽  
Differential Polynomials ◽  
Extended Selberg Class

Relying on Nevanlinna theory and the properties of L-functions in the extended Selberg class, we mainly study the uniqueness problems on L-functions concerning certain differential polynomials. This generalizes some results of Steuding, Li, Fang, and Liu-Li-Yi.

On the structure of the Selberg class, V: 1 < d < 5/3

2002 ◽  
Vol 150 (3) ◽  
pp. 485-516 ◽  
Author(s):  
Jerzy Kaczorowski ◽  
Alberto Perelli
Keyword(s):  
Selberg Class ◽  
Class V

ON INTERPOLATION FUNCTIONS FOR GENERALIZED Li COEFFICIENTS IN THE SELBERG CLASS

2011 ◽  
Vol 07 (03) ◽  
pp. 771-792
Author(s):  
ALMASA ODŽAK ◽  
LEJLA SMAJLOVIĆ
Keyword(s):  
Exponential Type ◽  
Entire Functions ◽  
Complex Function ◽  
Zeta Functions ◽  
Unitary Representations ◽  
Selberg Class ◽  
Interpolation Function ◽  
Entire Complex ◽  
Class Of Functions ◽  
Interpolation Functions

We prove that there exists an entire complex function of order one and finite exponential type that interpolates the Li coefficients λF(n) attached to a function F in the class [Formula: see text] that contains both the Selberg class of functions and (unconditionally) the class of all automorphic L-functions attached to irreducible, cuspidal, unitary representations of GL n(ℚ). We also prove that the interpolation function is (essentially) unique, under generalized Riemann hypothesis. Furthermore, we obtain entire functions of order one and finite exponential type that interpolate both archimedean and non-archimedean contribution to λF(n) and show that those functions can be interpreted as zeta functions built, respectively, over trivial zeros and all zeros of a function [Formula: see text].

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