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A family of Zeta functions built as Dirichlet series over the Riemann zeros are shown to
have meromorphic extensions in the whole complex plane, for which numerous analytical
features (the polar structures, plus countably many special values) are explicitly
displayed.
This work is about a generalization of Kœcher’s zeta function. Let be an Euclidean simple Jordan algebra of dimension and rank , an Euclidean space of dimension , a regular self-adjoint representation of in , the quadratic form associated to , the symmetric cone associated to and its automorphism group() Assume that and have -structures and respectively and is defined over . Let be a lattice in . The zeta series associated to and is defined bywhere ,...
In a previous article we studied the spectrum of the Zhang-Zagier height [2]. The progress we made stood on an algorithm that produced polynomials with a small height. In this paper we describe a new algorithm that provides even smaller heights. It allows us to find a limit point less than i.e. better than the previous one, namely . After some definitions we detail the principle of the algorithm, the results it gives and the construction that leads to this new limit point.
In this article, we formalize Z-module, that is a module over integer ring. Z-module is necassary for lattice problems, LLL (Lenstra-Lenstra-Lovász) base reduction algorithm and cryptographic systems with lattices [11].
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