Simultaneous nonvanishing of products of L-functions associated to elliptic cusp forms
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 suffic...
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| Hauptverfasser: | , , |
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| Dokumenttyp: | Article (Journal) |
| Sprache: | Englisch |
| Veröffentlicht: |
5 February 2020
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| In: |
Journal of mathematical analysis and applications
Year: 2020, Jahrgang: 486, Heft: 2 |
| ISSN: | 1096-0813 |
| DOI: | 10.1016/j.jmaa.2020.123930 |
| Online-Zugang: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1016/j.jmaa.2020.123930 Verlag, lizenzpflichtig, Volltext: http://www.sciencedirect.com/science/article/pii/S0022247X20300925 
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| Verfasserangaben: | YoungJu Choie, Winfried Kohnen, Yichao Zhang |
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| 520 | |a 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. | ||
| 650 | 4 | |a Double Eisenstein series | |
| 650 | 4 | |a Elliptic cusp forms | |
| 650 | 4 | |a Kernel function | |
| 650 | 4 | |a Products of -functions | |
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