Zeros of polynomials of derivatives of zeta functions
Takashi Nakamura

TL;DR
This paper investigates the zeros of polynomial combinations of derivatives of zeta functions, showing they have infinitely many zeros in a specific strip when the functions are hybridly universal, and provides bounds on their number.
Contribution
It establishes the existence of infinitely many zeros for polynomial derivatives of zeta functions under hybrid universality and analyzes zero bounds.
Findings
Infinitely many zeros in the strip 1/2 < Re(s) < 1 for certain polynomial combinations.
Zero bounds for these polynomial functions and their derivatives.
Extension to derivatives of polynomials of L-functions.
Abstract
Let be a polynomial whose coefficients are the ring of all general Dirichlet series which converge absolutely in the half-plane . In the present paper, we show that the function has infinitely many zeros in the vertical strip if is hybridly universal and is a polynomial such that at least one of the degree of is greater than zero. As a corollary, we prove that the function with has infinitely many zeros in the strip when is hybridly universal and is a polynomial with degree greater than zero. The upper bounds for the numbers of zeros of and…
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Taxonomy
TopicsAnalytic Number Theory Research · Advanced Mathematical Identities · Meromorphic and Entire Functions
