GAPS BETWEEN THE ZEROS OF EPSTEIN'S ZETA-FUNCTIONS ON THE CRITICAL LINE

2005 ◽  
Vol 37 (01) ◽  
pp. 45-53 ◽  
Author(s):  
M. JUTILA ◽  
K. SRINIVAS
Keyword(s):  
Critical Line ◽  
Zeta Functions

scholarly journals Zeros of quadratic zeta-functions on the critical line

1995 ◽  
Vol 69 (1) ◽  
pp. 21-38 ◽  
Author(s):  
A. Sankaranarayanan
Keyword(s):  
Critical Line ◽  
Zeta Functions

scholarly journals On complex zeros off the critical line for non-monomial polynomial of zeta-functions

2016 ◽  
Vol 284 (1-2) ◽  
pp. 23-39 ◽  
Author(s):  
Takashi Nakamura ◽  
Łukasz Pańkowski
Keyword(s):  
Critical Line ◽  
Zeta Functions ◽  
Complex Zeros

scholarly journals The fourth moment of individual Dirichlet L-functions on the critical line

2020 ◽  
Author(s):  
Berke Topacogullari
Keyword(s):  
Critical Line ◽  
Power Saving ◽  
Zeta Functions ◽  
Number Fields ◽  
Fourth Moment ◽  
Quadratic Number ◽  
Second Moment ◽  
Dirichlet Characters ◽  
Asymptotic Formulae ◽  
Special Cases

Abstract We prove an asymptotic formula for the second moment of a product of two Dirichlet L-functions on the critical line, which has a power saving in the error term and which is uniform with respect to the involved Dirichlet characters. As special cases we give uniform asymptotic formulae for the fourth moment of individual Dirichlet L-functions and for the second moment of Dedekind zeta functions of quadratic number fields on the critical line.

scholarly journals A note on the gaps between zeros of Epstein's zeta-functions on the critical line

2017 ◽  
Vol 57 (2) ◽  
pp. 235-253
Author(s):  
Stephan Baier ◽  
Srinivas Kotyada ◽  
Usha Keshav Sangale
Keyword(s):  
Critical Line ◽  
Zeta Functions

Mean values of certain zeta-functions on the critical line

1990 ◽  
Vol 29 (4) ◽  
pp. 351-360
Author(s):  
A. Ivic ◽  
A. Perelli
Keyword(s):  
Critical Line ◽  
Zeta Functions ◽  
Mean Values

scholarly journals On the zeros of Epstein zeta functions

2014 ◽  
Vol 26 (6) ◽  
Author(s):  
Yoonbok Lee
Keyword(s):  
Quadratic Form ◽  
Lower Bounds ◽  
Critical Line ◽  
Zeta Functions ◽  
Upper Bounds ◽  
Positive Definite ◽  
Asymptotic Formulas ◽  
Positive Definite Quadratic Form ◽  
Number Of Zeros ◽  
Existence Of Zeros

AbstractWe investigate the zeros of Epstein zeta functions associated with a positive definite quadratic form with rational coefficients. Davenport and Heilbronn, and also Voronin, proved the existence of zeros of Epstein zeta functions off the critical line when the class number of the quadratic form is bigger than 1. These authors give lower bounds for the number of zeros in strips that are of the same order as the more easily proved upper bounds. In this paper, we improve their results by providing asymptotic formulas for the number of zeros.

scholarly journals EPSTEIN ZETA-FUNCTIONS, SUBCONVEXITY, AND THE PURITY CONJECTURE

2018 ◽  
Vol 19 (2) ◽  
pp. 581-596 ◽  
Author(s):  
Valentin Blomer
Keyword(s):  
Eisenstein Series ◽  
Quadratic Forms ◽  
Critical Line ◽  
Zeta Functions ◽  
Subconvexity Bounds

Subconvexity bounds on the critical line are proved for general Epstein zeta-functions of $k$-ary quadratic forms. This is related to sup-norm bounds for unitary Eisenstein series on $\text{GL}(k)$ associated with the maximal parabolic of type $(k-1,1)$, and the exact sup-norm exponent is determined to be $(k-2)/8$ for $k\geqslant 4$. In particular, if $k$ is odd, this exponent is not in $\frac{1}{4}\mathbb{Z}$, which is relevant in the context of Sarnak’s purity conjecture and shows that it can in general not directly be generalized to Eisenstein series.

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