Minima of Epstein’s Zeta function and heights of flat tori

2006 ◽  
Vol 165 (1) ◽  
pp. 115-151 ◽  
Author(s):  
Peter Sarnak ◽  
Andreas Strömbergsson
Keyword(s):  
Zeta Function ◽  
Flat Tori

Certain Subclasses of Bi-Univalent Functions Involving Double Zeta Function

2015 ◽  
Vol 4 (4) ◽  
pp. 28-33
Author(s):  
Dr. T. Ram Reddy ◽  
◽  
R. Bharavi Sharma ◽  
K. Rajya Lakshmi ◽  
◽  
...  
Keyword(s):  
Zeta Function ◽  
Univalent Functions ◽  
Double Zeta

Universality of $L$-Dirichlet functions and nontrivial zeros of the Riemann zeta-function

2019 ◽  
Vol 210 (12) ◽  
pp. 1753-1773 ◽  
Author(s):  
A. Laurinčikas ◽  
J. Petuškinaitė
Keyword(s):  
Zeta Function ◽  
Riemann Zeta Function ◽  
Nontrivial Zeros ◽  
The Riemann Zeta Function ◽  
Riemann Zeta

The (α, β)-ramification invariants of a number field

2021 ◽  
Vol 71 (1) ◽  
pp. 251-263
Author(s):  
Guillermo Mantilla-Soler
Keyword(s):  
Zeta Function ◽  
Number Field ◽  
Residue Class ◽  
Interesting Application ◽  
Dedekind Zeta Function ◽  
Arithmetic Properties

Abstract Let L be a number field. For a given prime p, we define integers α p L $ \alpha_{p}^{L} $ and β p L $ \beta_{p}^{L} $ with some interesting arithmetic properties. For instance, β p L $ \beta_{p}^{L} $ is equal to 1 whenever p does not ramify in L and α p L $ \alpha_{p}^{L} $ is divisible by p whenever p is wildly ramified in L. The aforementioned properties, although interesting, follow easily from definitions; however a more interesting application of these invariants is the fact that they completely characterize the Dedekind zeta function of L. Moreover, if the residue class mod p of α p L $ \alpha_{p}^{L} $ is not zero for all p then such residues determine the genus of the integral trace.

scholarly journals A zeta function related to the transition matrix of the discrete-time quantum walk on a graph

2021 ◽  
Vol 344 (7) ◽  
pp. 112412
Author(s):  
Norio Konno ◽  
Iwao Sato ◽  
Etsuo Segawa
Keyword(s):  
Zeta Function ◽  
Discrete Time ◽  
Transition Matrix ◽  
Quantum Walk ◽  
Time Quantum

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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