On zeros of approximate functions of the Rankin–Selberg L-functions
نویسندگان
چکیده
منابع مشابه
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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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In this paper we study the possibility of real zeros near s = 1 for the RankinSelberg L-functions L(s, f × g) and L(s, sym(g) × sym(g)), where f, g are newforms, holomorphic or otherwise, on the upper half plane H, and sym(g) denotes the automorphic form on GL(3)/Q associated to g by Gelbart and Jacquet ([GJ79]). We prove that the set of such zeros of these L-functions is the union of the corre...
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In [1], Epstein, Sarnak, and I gave some general results concerning the zeros of an L-function attached to an even Maass wave form for T = PSL(2, Z). The main result was that such an L-function has many zeros on its critical line. In fact, we showed that the analogue of the Hardy-Littlewood theorem for the Riemann zeta function holds for these L-functions as well. In this note I announce the ne...
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ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 2009
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa136-1-3