On zeros of cubic L-functions
نویسندگان
چکیده
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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Introduction. As we have shown several years ago [Y2], zeros of L(s,∆) and L(s,∆) can be calculated quite efficiently by a certain experimental method. Here ∆ denotes the cusp form of weight 12 with respect to SL(2,Z) and L(s,∆) (resp. L(s,∆)) denotes the standard (resp. symmetric square) L-function attached to ∆. The purpose of this paper is to show that this method can be applied to a wide cl...
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Assuming the grand Riemann hypothesis, we investigate the distribution of the lowlying zeros of the L-functions L(s, ψ), where ψ is a character of the ideal class group of the imaginary quadratic field Q( √ −D) (D squarefree, D > 3, D ≡ 3 (mod 4)). We prove that, in the vicinity of the central point s = 1/2, the average distribution of these zeros (for D −→ ∞) is governed by the symplectic dist...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2007
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2006.10.006