Expansion of Dirichlet L-function on the critical line in Meixner-Pollaczek polynomials

2014/12/03 by Hiroto Inoue, Inoue, Hiroto
Mathematics · #Advanced Mathematical Identities #Analytic Number Theory Research #Boundary value problem #Critical line #Dirichlet L-function #Dirichlet distribution #Dirichlet series #FOS: Mathematics #Mathematical analysis #Mathematics #Meromorphic and Entire Functions #Multiplicative function #Orthogonal polynomials #Pure mathematics #Representation Theory (math.RT) #Riemann zeta function #math.RT

paper · pdf · doi:10.48550/arxiv.1412.1220

14 pages

arxiv created 2014/12/03 · openalex publication_date 2014/12/03 · arxiv updated 2014/12/04 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We study the expansions of the completed Riemann zeta function and completed Dirichlet L-functions in Meixner-Pollaczek polynomials. We give the proof of the uniform convergence, the multiplicative structure for the coefficients of these expansions, and a calculation for the coefficients of a completed Dirichlet L-function L(s, χ_-1). Furthermore, we give a boundary for the zeros of the approximating polynomial.

Citations

• Mellin transforms and asymptotics: Harmonic sums

Related

• Extreme values of the Dirichlet L-functions at the critical points of the Riemann zeta function
• Expansions of the Riemann Zeta function in the critical strip
• Explicit Upper Bounds for L-functions on the critical line
• Orthogonal polynomial expansions for the Riemann xi function
• A new expansion of the Riemann zeta function