Non-positivity of Certain Functions Associated with Analysis on Elliptic Surfaces
نویسنده
چکیده
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.
منابع مشابه
Nonpositivity of Certain Functions Associated with Analysis on Elliptic Surface
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, this term is the Laplace transform of certain infinite series consisting of KBessel functions. The positivity property of the fourth log derivative of such series is closely related to the Riemann hypothesis for the Hasse-Weil L-funct...
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