On the Linnik-Sprindžuk theorem about the zeros of L-functions

J. Kaczorowski; A. Perelli

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Displaying similar documents to “On the Linnik-Sprindžuk theorem about the zeros of L-functions”

On the zeros of the Riemann $ξ$ -function.

Csordas, George, Yang, Chung-Chun (2003)

Southwest Journal of Pure and Applied Mathematics [electronic only]

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Large gaps between consecutive zeros of the Riemann zeta-function. II

H. M. Bui (2014)

Acta Arithmetica

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Assuming the Riemann Hypothesis we show that there exist infinitely many consecutive zeros of the Riemann zeta-function whose gaps are greater than 2.9 times the average spacing.

An Asymptotic Formula for a sum Involving Zeros of the Riemann Zeta-function

Yuichi Kamiya, Masatoshi Suzuki (2004)

Publications de l'Institut Mathématique

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A note on moments of $ζ^{'} (1 / 2 + i γ)$ .

Laurinčikas, Antanas, Steuding, Jörn (2004)

Publications de l'Institut Mathématique. Nouvelle Série

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Pair correlation of the zeros of the Riemann zeta function in longer ranges

Tsz Ho Chan (2004)

Acta Arithmetica

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Counting distinct zeros of the Riemann zeta-function.

Farmer, David W. (1995)

The Electronic Journal of Combinatorics [electronic only]

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On the exact location of the non-trivial zeros of Riemann's zeta function

Juan Arias de Reyna, Jan van de Lune (2014)

Acta Arithmetica

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We introduce the real valued real analytic function κ(t) implicitly defined by $e^{2 π i κ (t)} = - e^{- 2 i ϑ (t)} (ζ^{'} (1 / 2 - i t)) / (ζ^{'} (1 / 2 + i t))$ (κ(0) = -1/2). By studying the equation κ(t) = n (without making any unproved hypotheses), we show that (and how) this function is closely related to the (exact) position of the zeros of Riemann’s ζ(s) and ζ’(s). Assuming the Riemann hypothesis and the simplicity of the zeros of ζ(s), it follows that the ordinate of the zero 1/2 + iγₙ of ζ(s) is the unique solution to the equation κ(t) = n.

On the zeros of degree one L-functions from the extended Selberg class

Haseo Ki, Yoonbok Lee (2011)

Acta Arithmetica

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Some conjectures on the zeros of approximates to the Riemann ≡-function and incomplete gamma functions

James Haglund (2011)

Open Mathematics

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Riemann conjectured that all the zeros of the Riemann ≡-function are real, which is now known as the Riemann Hypothesis (RH). In this article we introduce the study of the zeros of the truncated sums ≡N(z) in Riemann’s uniformly convergent infinite series expansion of ≡(z) involving incomplete gamma functions. We conjecture that when the zeros of ≡N(z) in the first quadrant of the complex plane are listed by increasing real part, their imaginary parts are monotone nondecreasing. We show...

Nearest neighbor spacing distributions for the zeros of the real or imaginary part of the Riemann xi-function on vertical lines

Masatoshi Suzuki (2015)

Acta Arithmetica

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We show that the density functions of nearest neighbor spacing distributions for the zeros of the real or imaginary part of the Riemann xi-function on vertical lines are described by the M-function which appears in value distribution of the logarithmic derivative of the Riemann zeta-function on vertical lines.