2020/01/31 by YoungJu Choie, Winfried Kohnen, Choie, YoungJu +3
Mathematics · #11F30 #11F67 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Complex Variables (math.CV) #FOS: Mathematics #Mathematics Subject Classification: primary 11F11 #Number Theory (math.NT) #secondary 11F99
paper · pdf · doi:10.48550/arxiv.2002.00096
openalex publication_date 2020/01/31 · openalex created_date 2020/02/07 · openalex updated_date 2026/07/28
A generalized Riemann hypothesis states that all zeros of the completed Hecke L-function L^*(f,s) of a normalized Hecke eigenform f on the full modular group should lie on the vertical line Re(s)=(k)/(2). It was shown by Kohnen that there exists a Hecke eigenform f of weight k such that L^*(f,s) ≠ 0 for sufficiently large k and any point on the line segments Im(s)=t0, (k-1)/(2) < Re(s) < (k)/(2)-ε, (k )/(2)+ε< Re(s) < (k+1)/(2), for any given real number t0 and a positive real number ε. This paper concerns the non-vanishing of the product L^*(f,s)L^*(f,w) (s,w∈ ℂ) on average.