The Mean Values and the Universality of Rankin-Selberg L-Functions
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منابع مشابه
Strong exponent bounds for the local Rankin-Selberg convolution
Let $F$ be a non-Archimedean locally compact field. Let $sigma$ and $tau$ be finite-dimensional representations of the Weil-Deligne group of $F$. We give strong upper and lower bounds for the Artin and Swan exponents of $sigmaotimestau$ in terms of those of $sigma$ and $tau$. We give a different lower bound in terms of $sigmaotimeschecksigma$ and $tauotimeschecktau$. Using the Langlands...
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In this paper we calculate the asymptotics of various moments of the central values of Rankin-Selberg convolution L-functions of large level, thus generalizing the results and methods of W. Duke, J. Friedlander, and H. Iwaniec and of the authors. Consequences include convexity-breaking bounds, nonvanishing of a positive proportion of central values, and linear independence results for certain H...
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In this paper, we find a relation between the proportionality factors which arise from the functional equations of two families of local Rankin-Selberg convolutions for irreducible admissible representations of orthogonal groups, or unitary groups. One family is that of local integrals of the doubling method, and the other family is that of local integrals expressed in terms of sph...
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In this paper, some asymptotic formulas are proved for the harmonic mollified second moment of a family of Rankin-Selberg Lfunctions. One of the main new input is a substantial improvement of the admissible length of the mollifier which is done by solving a shifted convolution problem by a spectral method on average. A first consequence is a new subconvexity bound for Rankin-Selberg L-functions...
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The values of L-functions at special points have been the subject of intensive studies. For example, a good positive lower bound for the central value of Hecke L-functions would rule out the existence of the Landau-Siegel zero, see the notable paper [IS]; the nonvanishing of certain Rankin-Selberg L-functions is a crucial ingredient in the current development of the generalized Ramanujan conjec...
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