We prove an asymptotic formula for the fourth moment of automorphic L-functions of level , where p is a fixed prime number and ν → ∞. This is a continuation of work by Rouymi, who computed the asymptotics of the first three moments at a prime power level, and a generalization of results obtained for a prime level by Duke, Friedlander Iwaniec and Kowalski, Michel VanderKam.
In this paper we propose an original approach for the simulation of the time-dependent response of a floating elastic plate using the so-called Singularity Expansion Method. This method consists in computing an asymptotic behaviour for large time obtained by means of the Laplace transform by using the analytic continuation of the resolvent of the problem. This leads to represent the solution as the sum of a discrete superposition of exponentially damped oscillating motions associated to the poles...
We study the quadratic case of a conjecture made by Van der Geer and Schoof about the behaviour of certain functions which are defined over the group of Arakelov divisors of a number field. These functions correspond to the standard function for divisors of algebraic curves and we prove that they reach their maximum value for principal Arakelov divisors and nowhere else. Moreover, we consider a function , which is an analogue of exp defined on the class group, and we show it also assumes its...
Let be the Riemann zeta-function. If and , then it is known that the inequality is valid except at the zeros of . Here we investigate the Lerch zeta-function which usually has many zeros off the critical line and it is expected that these zeros are asymmetrically distributed with respect to the critical line. However, for equal parameters it is still possible to obtain a certain version of the inequality .