Simultaneous nonvanishing of products of L-functions associated to elliptic cusp forms

• Verfasst von: Ch'oe, Yŏng-ju [VerfasserIn]
• Verfasst von: Kohnen, Winfried [VerfasserIn]
• Verfasst von: Zhang, Yichao [VerfasserIn]
• Titel: Simultaneous nonvanishing of products of L-functions associated to elliptic cusp forms
• Verf.angabe: YoungJu Choie, Winfried Kohnen, Yichao Zhang
• E-Jahr: 2020
• Jahr: 5 February 2020
• Umfang: 14 S.
• Fussnoten: Gesehen am 20.04.2020
• Titel Quelle: Enthalten in: Journal of mathematical analysis and applications
• Ort Quelle: Amsterdam [u.a.] : Elsevier, 1960
• Jahr Quelle: 2020
• Band/Heft Quelle: 486(2020,2) Artikel-Nummer 123930, Seite 1-14
• ISSN Quelle: 1096-0813
• DOI: doi:10.1016/j.jmaa.2020.123930
• Datenträger: Online-Ressource
• Sprache: eng
• Sach-SW: Double Eisenstein series
• Sach-SW: Elliptic cusp forms
• Sach-SW: Kernel function
• Sach-SW: Products of -functions
• K10plus-PPN: 1694969762

Abstract

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)=k2. It was shown in [6] 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−12<Re(s)<k2−ϵ,k2+ϵ<Re(s)<k+12, 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.