Simple Zeros of the Riemann Zeta-Function

1998 ◽  
Vol 76 (3) ◽  
pp. 497-522 ◽  
Author(s):  
JB Conrey ◽  
A Ghosh ◽  
SM Gonek
Keyword(s):  
Zeta Function ◽  
Riemann Zeta Function ◽  
Simple Zeros ◽  
The Riemann Zeta Function ◽  
Riemann Zeta

scholarly journals Counting distinct zeros of the Riemann zeta-function

10.37236/1195 ◽  
1994 ◽  
Vol 2 (1) ◽  
Author(s):  
David W. Farmer
Keyword(s):  
Zeta Function ◽  
Riemann Zeta Function ◽  
Simple Zeros ◽  
The Riemann Zeta Function ◽  
Riemann Zeta ◽  
Derivatives Of

Bounds on the number of simple zeros of the derivatives of a function are used to give bounds on the number of distinct zeros of the function.

scholarly journals On the integer part of the reciprocal of the Riemann zeta function tail at certain rational numbers in the critical strip

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
WonTae Hwang ◽  
Kyunghwan Song
Keyword(s):  
Zeta Function ◽  
Rational Number ◽  
Riemann Zeta Function ◽  
Rational Numbers ◽  
Critical Strip ◽  
Integer Part ◽  
Integral Points ◽  
The Riemann Zeta Function ◽  
Riemann Zeta

Abstract We prove that the integer part of the reciprocal of the tail of $\zeta (s)$ ζ ( s ) at a rational number $s=\frac{1}{p}$ s = 1 p for any integer with $p \geq 5$ p ≥ 5 or $s=\frac{2}{p}$ s = 2 p for any odd integer with $p \geq 5$ p ≥ 5 can be described essentially as the integer part of an explicit quantity corresponding to it. To deal with the case when $s=\frac{2}{p}$ s = 2 p , we use a result on the finiteness of integral points of certain curves over $\mathbb{Q}$ Q .

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