Value distribution for the derivatives of the logarithm of L-functions from the Selberg class in the half-plane of absolute convergence

2015/01/09 by Takashi Nakamura, Nakamura, Takashi, Łukasz Pańkowski +1
Mathematics · #11M06 #11M26 #Analytic Number Theory Research #Analytic and geometric function theory #FOS: Mathematics #Meromorphic and Entire Functions #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1501.02045

openalex publication_date 2015/01/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In the present paper, we show that, for every δ>0, the function (log L(s))^(m), where m∈ ℕ ∪ \ 0\ and L (s) := ∑_n=1^∞ a(n) n^-s is an element of the Selberg class S, takes any value infinitely often in any strip 10. In particular, L (s) takes any non-zero value infinitely often in the strip 1

Citations

• Numerical computations on the zeros of the Euler double zeta-function I

Related

• Zeros near s=1 and the constant term of L'/L for L-functions in the Selberg class
• Selberg's central limit theorem of L-functions near the critical line
• Universality for the iterated integrals of logarithms of L-functions in the Selberg class
• Conditional estimates for L-functions in the Selberg class
• Joint Extreme values of L-functions