Non-positivity of certain functions associated with analysis on elliptic surfaces
| dc.creator | Suzuki, Masatoshi | |
| dc.date | 2007-03-02 | |
| dc.date | 2008-05-29 | |
| dc.date.accessioned | 2026-07-07T09:41:25Z | |
| dc.date.available | 2026-07-07T09:41:25Z | |
| dc.description | In this paper, we study some basic analytic properties of the boundary term of Fesenko's two-dimensional zeta integrals. In the case of the rational number field, we show that this term is the Laplace transform of certain infinite series consisting of $K$-Bessel functions. It is known that the non-positivity property of the fourth log derivative of such series is a sufficient condition for the Riemann hypothesis of the Hasse-Weil $L$-function attached to an elliptic curve. We show that such non-positivity is a necessary condition under some technical assumption. | |
| dc.description | 28 pages | |
| dc.identifier | https://arxiv.org/abs/math/0703052 | |
| dc.identifier | http://arxiv.org/abs/math/0703052 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/161820 | |
| dc.subject | Number Theory | |
| dc.subject | 11G40, 11M36, 11M41 | |
| dc.title | Non-positivity of certain functions associated with analysis on elliptic surfaces | |
| dc.type | text |