The Riemann hypothesis for certain integrals of Eisenstein series
| dc.creator | Lagarias, Jeffrey C. | |
| dc.creator | Suzuki, Masatoshi | |
| dc.date | 2004-12-02 | |
| dc.date | 2005-11-03 | |
| dc.date.accessioned | 2026-07-07T06:39:06Z | |
| dc.date.available | 2026-07-07T06:39:06Z | |
| dc.description | This paper studies the non-holomorphic Eisenstein series E(z,s) for the modular surface, and shows that integration with respect to certain non-negative measures gives meromorphic functions of s that have all their zeros on the critical line Re(s) = 1/2. For the constant term of the Eisenstein series it shows that all zeros are on the critical line for fixed y= Im(z) \ge 1, except possibly for two real zeros, which are present if and only if y > 4 πe^{-γ} = 7.0555+. It shows the Riemann hypothesis holds for all truncation integrals with truncation parameter T \ge 1. For T=1 this proves the Riemann hypothesis for a zeta function recently introduced by Lin Weng, attached to rank 2 semistable lattices over the rationals. | |
| dc.description | 23 pages; corrected residues of functions in theorem 1 and 2, added reference; v3 small corrections, removed uncited references; v4 more small corrections | |
| dc.identifier | https://arxiv.org/abs/math/0412039 | |
| dc.identifier | http://arxiv.org/abs/math/0412039 | |
| dc.identifier | J. Number Theory 118 (2006) 98-122 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/100962 | |
| dc.subject | Number Theory | |
| dc.title | The Riemann hypothesis for certain integrals of Eisenstein series | |
| dc.type | text |