منابع مشابه
Superposition of zeros of distinct L-functions
In this paper we ®rst prove a weighted prime number theorem of an ``o ̈-diagonal'' type for Rankin-Selberg L-functions of automorphic representations of GLm and GLm 0 over Q. Then for m 1, or under the Selberg orthonormality conjecture for mV 2, we prove that nontrivial zeros of distinct primitive automorphic L-functions for GLm over Q are uncorrelated, for certain test functions whose Fourier...
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For many L-functions of arithmetic interest, the values on or close to the edge of the region of absolute convergence are of great importance, as shown for instance by the proof of the Prime Number Theorem (equivalent to non-vanishing of ζ(s) for Re(s) = 1). Other examples are the Dirichlet L-functions (e.g., because of the Dirichlet class-number formula) and the symmetric square L-functions of...
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A small part of the Generalized Riemann Hypothesis asserts that L-functions do not have zeros on the line segment ( 2 , 1]. The question of vanishing at s = 2 often has deep arithmetical significance, and has been investigated extensively. A persuasive view is that L-functions vanish at 2 either for trivial reasons (the sign of the functional equation being negative), or for deep arithmetical r...
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ژورنال
عنوان ژورنال: Proceedings of the London Mathematical Society
سال: 2014
ISSN: 0024-6115
DOI: 10.1112/plms/pdu041