Real zeros and size of Rankin-Selberg L-functions in the level aspect
نویسندگان
چکیده
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 in the level aspect. Moreover, infinitely many Rankin-Selberg L-functions having at most eight non-trivial real zeros are produced and some new non-trivial estimates for the analytic rank of the family studied are obtained.
منابع مشابه
Rankin-selberg L-functions in the Level Aspect
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...
متن کاملStrong 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...
متن کاملSuperposition 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...
متن کاملThe Second Moment of Gl(3)×gl(2) L-functions, Integrated
We consider the family of Rankin-Selberg convolution L-functions of a fixed SL(3,Z) Maass form with the family of Hecke-Maass cusp forms on SL(2,Z). We estimate the second moment of this family of L-functions with a “long” integration in t-aspect. These L-functions are distinguished by their high degree (12) and large conductors (of size T ).
متن کاملOn local gamma factors for orthogonal groups and unitary groups
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...
متن کامل