Paper Info
Title
Distribution of a cotangent sum related to the Nyman-Beurling criterion for the Riemann Hypothesis.
Abstract
A certain category of cotangent sums has been proven of importance in the Nyman–Beurling criterion for the Riemann Hypothesis. In previous work ([12], [13]) the authors proved the existence of a unique positive measure μ on R, with respect to which certain normalized cotangent sums, evaluated at rational numbers with fixed denominators are equidistributed. The tools applied in this paper belong to various fields of Mathematics, for instance the relation between the equidistribution mod1 of the multiples of a number and the Diophantine approximation properties of that number. In this paper we prove an analogous result for the case that the denominator of the rational numbers is a fixed prime number and that the numerator is also prime.
Year
DOI
Venue
2019
10.1016/j.amc.2019.124589
Applied Mathematics and Computation
Keywords
Field
DocType
Cotangent sums,Equidistribution,Estermann zeta function,Riemann zeta function,Riemann Hypothesis,Exponential sums in finite fields
Prime (order theory),Rational number,Prime number,Riemann zeta function,Equidistributed sequence,Mathematical analysis,Pure mathematics,Riemann hypothesis,Mathematics,Fraction (mathematics),Diophantine approximation
Journal
Volume
ISSN
Citations 
363
0096-3003
0
PageRank 
References 
Authors
0.34
0
2
Name
Order
Citations
PageRank
Helmut Maier100.34
Michael Th. Rassias2115.24