On the zeros of linear combinations of derivatives of the Riemann zeta function, II

K. Paolina Koutsaki, Albert Tamazyan, Alexandru Zaharescu

Type: Article

Publication Date: 2017-08-07

Citations: 1

DOI: https://doi.org/10.1142/s1793042118500252

Abstract

The relevant number to the Dirichlet series [Formula: see text], is defined to be the unique integer [Formula: see text] with [Formula: see text], which maximizes the quantity [Formula: see text]. In this paper, we classify the set of all relevant numbers to the Dirichlet [Formula: see text]-functions. The zeros of linear combinations of [Formula: see text] and its derivatives are also studied. We give an asymptotic formula for the supremum of the real parts of zeros of such combinations. We also compute the degree of the largest derivative needed for such a combination to vanish at a certain point.

Locations

International Journal of Number Theory - View - PDF

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+	More Zeros of the Derivatives of the Riemann Zeta Function on the Left Half Plane	2013	Ricky E. Farr Sebastian Pauli
+	Multiplicative Number Theory	1980	H. Davenport
+ PDF Chat	Transcendental Number Theory	1975	A. Baker
+	Uniform distribution of sequences	1974	L. Kuipers Harald Niederreiter
+	Geometrisches zur Riemannschen Zetafunktion	1935	Andreas Speiser
+ PDF Chat	Zeros of the derivatives of the Riemann zeta-function	1974	Norman Levinson Hugh L. Montgomery
+ PDF Chat	Formulas for higher derivatives of the Riemann zeta function	1985	Tom M. Apostol
+	Zero-free regions of derivatives of Riemann zeta function	1982	Disha Verma Amarjit Kaur
+	Another Zero-Free Region for ζ (k) (s)	1970	Robert Spira
+ PDF Chat	An introduction to the theory of numbers	1960	G. H. Hardy