Some new density theorems for Dirichlet $L$-functions

J. Pintz

Type: Article

Publication Date: 2019-01-01

Citations: 2

DOI: https://doi.org/10.4064/bc118-14

Abstract

We prove some new log-free density theorems for zeros of Dirichlet L-functions (which accordingly are more sharp than earlier ones near to the boundary line of the critical strip). The results can be applied in several problems of prime number theory.

Locations

Banach Center Publications - View - PDF
arXiv (Cornell University) - View - PDF

Similar Works

Action	Title	Year	Authors
+	Some new density theorems for Dirichlet L-functions	2018	J. Pintz
+	Some new density theorems for Dirichlet L-functions	2018	J. Pintz
+	Zero-Density Theorems for Families of Dirichlet $L$-functions	2022	C. C. Corrigan Liangyi Zhao
+ PDF Chat	Moments and zero density estimates for Dirichlet L-functions	2021	Keiju Sono
+	A note on Dirichlet $L$-functions	2017	John Friedlander Henryk Iwaniec
+	A note on Dirichlet $L$-functions	2017	John Friedlander Henryk Iwaniec
+	Weighted one-level density of low-lying zeros of Dirichlet $L$-functions	2022	Shingo Sugiyama Ade Irma Suriajaya
+	Limit Theorems for Dirichlet L-Functions	1996	Antanas Laurinčikas
+	Large values of Dirichlet polynomials and zero density estimates for the Riemann zeta function	2019	Bryce Kerr
+	A log-free zero-density estimate and small gaps in coefficients of $L$-functions	2013	Amir Akbary Timothy S. Trudgian
+	A log-free zero-density estimate and small gaps in coefficients of $L$-functions	2013	Amir Akbary Timothy S. Trudgian
+	L-Functions	1989	Toshitsune Miyake
+	A note on prime number races and zero free regions for $L$ functions	2020	Marco Aymone
+ PDF Chat	New large value estimates for Dirichlet polynomials	2024	Larry Guth James Maynard
+	Zeros of partial sums of $L$-functions.	2018	Arindam Roy Akshaa Vatwani
+ PDF Chat	Lower bounds for negative moments of Dirichlet $L$-functions to a fixed modulus	2024	Peng Gao
+	Zeros of partial sums of $L$-functions	2018	Arindam Roy Akshaa Vatwani
+	A note on the zeros of $L$-functions associated to fixed-order Dirichlet characters	2023	C. C. Corrigan
+	Counting zeros of Dirichlet $L$-functions	2020	Michael A. Bennett Greg Martin Kevin O’Bryant Andrew Rechnitzer
+	Counting Zeros of Dirichlet $L$-Functions	2020	Michael A. Bennett Greg Martin Kevin O’Bryant Andrew Rechnitzer

Works That Cite This (6)

Action	Title	Year	Authors
+ PDF Chat	Density estimates for the zeros of the Beurling ζ function in the critical strip	2022	Szilárd Gy. Révész
+ PDF Chat	Oscillation of the Remainder Term in the Prime Number Theorem of Beurling, “Caused by a Given ζ-Zero”	2022	Szilárd Gy. Révész
+ PDF Chat	A new explicit formula in the additive theory of primes with applications I. The explicit formula for the Goldbach problem and the Generalized Twin Prime Problem	2023	J. Pintz
+	An explicit log-free zero density estimate for the Riemann zeta-function	2024	Chiara Bellotti
+	Distribution of Beurling primes and zeroes of the Beurling zeta function I. Distribution of the zeroes of the zeta function of Beurling	2020	Szilárd Gy. Révész
+ PDF Chat	Zeros of dirichlet <i>L</i>‐functions near the critical line	2024	George E. Dickinson

Works Cited by This (7)

Action	Title	Year	Authors
+	Multiplicative Number Theory	1980	H. Davenport
+	HYBRID BOUNDS FOR DIRICHLET L-FUNCTIONS II	1980	D. R. Heath‐Brown
+ PDF Chat	Zero-Free Regions for Dirichlet L-Functions, and the Least Prime in an Arithmetic Progression	1992	D. R. Heath‐Brown
+	On the distribution of roots of Riemann zeta and allied functions, I	1969	Gábor Halász P. Túrán
+	Zero-free Regions for the Riemann Zeta Function	2024	Kevin Ford
+	THE RIEMANN ZETA-FUNCTION The Theory of the Riemann Zeta-Function with Applications	1986	Matti Jutila
+ PDF Chat	Topics in Multiplicative Number Theory	1971	Hugh L. Montgomery