On the zeros of the Epstein zeta-function on the critical line

2015 ◽  
Vol 70 (4) ◽  
pp. 785-787 ◽  
Author(s):  
I S Rezvyakova
Keyword(s):  
Zeta Function ◽  
Critical Line ◽  
Epstein Zeta Function

scholarly journals Zeros of the Epstein zeta function to the right of the critical line

2020 ◽  
pp. 1-12
Author(s):  
YOUNESS LAMZOURI
Keyword(s):  
Zeta Function ◽  
Error Term ◽  
Critical Line ◽  
Quadratic Field ◽  
Positive Definite ◽  
Real Numbers ◽  
Positive Definite Quadratic Form ◽  
Number Of Zeros ◽  
Epstein Zeta Function ◽  
The Right

Abstract Let E(s, Q) be the Epstein zeta function attached to a positive definite quadratic form of discriminant D < 0, such that h(D) ≥ 2, where h(D) is the class number of the imaginary quadratic field ${{\mathbb{Q}}(\sqrt D)}$ . We denote by N E (σ1, σ2, T) the number of zeros of E(s, Q) in the rectangle σ1 < Re(s) ≤ σ2 and T ≤ Im (s) ≤ 2T, where 1/2 < σ1 < σ2 < 1 are fixed real numbers. In this paper, we improve the asymptotic formula of Gonek and Lee for N E (σ1, σ2, T), obtaining a saving of a power of log T in the error term.

scholarly journals Minimal theta functions

1988 ◽  
Vol 30 (1) ◽  
pp. 75-85 ◽  
Author(s):  
Hugh L. Montgomery
Keyword(s):  
Functional Equation ◽  
Quadratic Form ◽  
Zeta Function ◽  
Theta Functions ◽  
Binary Quadratic Form ◽  
Positive Definite ◽  
Epstein Zeta Function ◽  
Image Position

Let be a positive definite binary quadratic form with real coefficients and discriminant b2 − 4ac = −1.Among such forms, let . The Epstein zeta function of f is denned to beRankin [7], Cassels [1], Ennola [5], and Diananda [4] between them proved that for every real s > 0,We prove a corresponding result for theta functions. For real α > 0, letThis function satisfies the functional equation(This may be proved by using the formula (4) below, and then twice applying the identity (8).)

scholarly journals Maximum of the Riemann Zeta Function on a Short Interval of the Critical Line

2018 ◽  
Vol 72 (3) ◽  
pp. 500-535 ◽  
Author(s):  
Louis-Pierre Arguin ◽  
David Belius ◽  
Paul Bourgade ◽  
Maksym Radziwiłł ◽  
Kannan Soundararajan
Keyword(s):  
Zeta Function ◽  
Riemann Zeta Function ◽  
Critical Line ◽  
Short Interval ◽  
The Riemann Zeta Function ◽  
Riemann Zeta

Small values of the Riemann zeta function on the critical line

2015 ◽  
Vol 169 (3) ◽  
pp. 201-220 ◽  
Author(s):  
Justas Kalpokas ◽  
Paulius Šarka
Keyword(s):  
Zeta Function ◽  
Riemann Zeta Function ◽  
Critical Line ◽  
The Riemann Zeta Function ◽  
Riemann Zeta
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