Non-positivity of certain functions associated with analysis on elliptic surfaces

dc.creatorSuzuki, Masatoshi
dc.date2007-03-02
dc.date2008-05-29
dc.date.accessioned2026-07-07T09:41:25Z
dc.date.available2026-07-07T09:41:25Z
dc.descriptionIn 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.description28 pages
dc.identifierhttps://arxiv.org/abs/math/0703052
dc.identifierhttp://arxiv.org/abs/math/0703052
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/161820
dc.subjectNumber Theory
dc.subject11G40, 11M36, 11M41
dc.titleNon-positivity of certain functions associated with analysis on elliptic surfaces
dc.typetext

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