SU\G(𝔸)/K·U

A note on zero density results implying large value estimates for Dirichlet polynomials

Kaisa Matomäki, Joni Teräväinen

Type: Preprint

Publication Date: 2024-03-19

Citations: 0

DOI: https://doi.org/10.48550/arxiv.2403.13157

Abstract

In this note we investigate connections between zero density estimates for the Riemann zeta function and large value estimates for Dirichlet polynomials. It is well known that estimates of the latter type imply estimates of the former type. Our goal is to show that there is an implication to the other direction as well, i.e. zero density estimates for the Riemann zeta function imply large value estimates for Dirichlet polynomials.

Locations

  • arXiv (Cornell University) - View - PDF

Similar Works

Action Title Year Authors
+ Large values of Dirichlet polynomials and zero density estimates for the Riemann zeta function 2019 Bryce Kerr
+ A note on the zero-density estimates for the zeta function 1979 Aleksandar Ivić
+ PDF Chat New large value estimates for Dirichlet polynomials 2024 Larry Guth
James Maynard
+ None 2000 Jean Bourgain
+ PDF Chat Large values of Dirichlet polynomials 1973 M. N. Huxley
+ An Aspect of the Zeta Function Zero Gap Estimates 2023
+ PDF Chat Large values of Dirichlet polynomials II 1975 M. N. Huxley
+ On the zeros of the Riemann zeta function of large multiplicity 2011 R. N. Boyarinov
+ Mean and large values of Dirichlet polynomials (chapter 7) 1994 Hugh L. Montgomery
+ On some mean value results for the Riemann zeta-function 1989 James Lee Hafner
A. Ivić
+ A Note on the Distribution of the Riemann Zeta Function Zeros 2024 Darrell Cox
Pedro Caceres
+ Discrepancy Theorems for the Zero Distribution of Rational Functions 2014 Regina Fieger
+ An Explicit Estimate in the Theory of the Distribution of the Zeros of the Riemann Zeta Function 2004 Akio Fujii
+ Density theorems for the zeta function 1971 Enrico Bombieri
+ A note on Dirichlet $L$-functions 2017 John Friedlander
Henryk Iwaniec
+ A note on Dirichlet $L$-functions 2017 John Friedlander
Henryk Iwaniec
+ PDF Chat Large values of Dirichlet polynomials, III 1975 M. N. Huxley
+ On values of the Riemann zeta function at positive integers 2019 Ayhan Dil
Khristo N. Boyadzhiev
Ilham A. Aliev
+ On Small Zeros of Dirichlet L-Functions 1975 P. Weinberger
+ Two theorems on the zero density of the riemann zeta function 1985 Yitang Zhang

Works That Cite This (0)

Action Title Year Authors

Works Cited by This (0)

Action Title Year Authors