scholarly journals Non-vanishing of high derivatives of automorphic L-functions at the center of the critical strip

2000 ◽  
Vol 2000 (526) ◽  
pp. 1-34 ◽  
Author(s):  
E. Kowalski ◽  
P. Michel ◽  
J. VanderKam
Keyword(s):  
Critical Strip ◽  
Derivatives Of

Nonvanishing of derivatives of Hecke $$L$$L-functions associated to cusp forms inside the critical strip

2018 ◽  
Vol 51 (2) ◽  
pp. 319-327
Author(s):  
Winfried Kohnen ◽  
Jyoti Sengupta ◽  
Miriam Weigel
Keyword(s):  
Cusp Forms ◽  
Critical Strip ◽  
Derivatives Of

scholarly journals ON THE MODULUS OF THE SELBERG ZETA-FUNCTIONS IN THE CRITICAL STRIP

2015 ◽  
Vol 20 (6) ◽  
pp. 852-865
Author(s):  
Andrius Grigutis ◽  
Darius Šiaučiūnas
Keyword(s):  
Riemann Surface ◽  
Modular Group ◽  
Compact Riemann Surface ◽  
Zeta Functions ◽  
Critical Strip ◽  
The Real ◽  
Derivatives Of ◽  
Logarithmic Derivatives

We investigate the behavior of the real part of the logarithmic derivatives of the Selberg zeta-functions ZPSL(2,Z)(s) and ZC (s) in the critical strip 0 < σ < 1. The functions ZPSL(2,Z)(s) and ZC (s) are defined on the modular group and on the compact Riemann surface, respectively.

scholarly journals On mean values and non-vanishing of derivatives of L-functions in a nonlinear family

2010 ◽  
Vol 147 (1) ◽  
pp. 19-34 ◽  
Author(s):  
Ritabrata Munshi
Keyword(s):  
Quadratic Form ◽  
Mean Value ◽  
Positive Definite ◽  
Critical Strip ◽  
Positive Definite Quadratic Form ◽  
Elliptic Fibrations ◽  
Mean Values ◽  
Cubic Polynomial ◽  
Derivatives Of

AbstractWe prove a mean-value result for derivatives of L-functions at the center of the critical strip for a family of forms obtained by twisting a fixed form by quadratic characters with modulus which can be represented as sum of two squares. Such a family of forms is related to elliptic fibrations given by the equation q(t)y2=f(x) where q(t)=t2+1 and f(x) is a cubic polynomial. The aim of the paper is to establish a prototype result for such quadratic families. Though our method can be generalized to prove similar results for any positive definite quadratic form in place of sum of two squares, we refrain from doing so to keep the presentation as clear as possible.

scholarly journals TWISTS OF AUTOMORPHIC L-FUNCTIONS AT THE CENTRAL POINT

2013 ◽  
Vol 09 (04) ◽  
pp. 1015-1053
Author(s):  
H. M. BUI
Keyword(s):  
Upper Bound ◽  
Central Point ◽  
Critical Strip ◽  
Primitive Character ◽  
Central Values ◽  
Positive Proportion ◽  
Primitive Forms ◽  
Derivatives Of

We study the nonvanishing of twists of automorphic L-functions at the center of the critical strip. Given a primitive character χ modulo D satisfying some technical conditions, we prove that the twisted L-functions L(f.χ, s) do not vanish at s = ½ for a positive proportion of primitive forms of weight 2 and level q, for large prime q. We also investigate the central values of high derivatives of L(f.χ, s), and from that derive an upper bound for the average analytic rank of the studied L-functions.

Physical Properties of TCNQ Salts with N-Methyl Derivatives of Pyridine

1982 ◽  
Vol 85 (1) ◽  
pp. 257-263 ◽  
Author(s):  
A. Graja ◽  
M. Przybylski ◽  
B. Butka ◽  
R. Swietlik
Keyword(s):  
Physical Properties ◽  
Methyl Derivatives ◽  
Derivatives Of
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