Inspired by Sun’s breakthrough in establishing the nonvanishing hypothesis for Rankin-Selberg convolutions for the groups GLn(R)×GLn−1(R) and GLn(C)×GLn−1(C), we confirm it for GLn(C)×GLn(C) at the central critical point.

We prove a sharp convexity bound for L-functions, at the centre of the critical strip, under conditions weaker than those for the Selberg Class. 2000 Mathematics Subject Classification: Primary 11M41

‎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...

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...

The Cauchy problem for the classical Dirac-Klein-Gordon system in two space dimensions is globally well-posed for L Schrödinger data and wave data in H 1 2 ×H − 1 2 . In the case of smooth data there exists a global smooth (classical) solution. The proof uses function spaces of Bourgain type based on Besov spaces – previously applied by Colliander, Kenig and Staffilani for generalized Benjamin-...

One way of characterizing Atle Selberg’s mathematical genius is that he had a “golden touch”. In those domains he thought about in depth, he saw further than generations before him, repeatedly uncovering truths lying below the surface. His breakthroughs on long-standing problems were based on imaginative and novel ideas which, once digested, were appreciated as simple and decisive. The impact o...

In this paper, we establish a general mean value result of arithmetic functions over short intervals with the Selberg-Delange method. As an application, we generalize the Deshouillers-Dress-Tenenbaum’s arcsin law on divisors to the short interval case.

X iv :1 00 3. 45 53 v2 [ m at h. N T ] 6 J un 2 01 0 ON SOME LOWER BOUNDS OF SOME SYMMETRY INTEGRALS by G.Coppola Abstract. We study the “symmetry integral”, say If , of some arithmetic functions f : N → R; we obtain from lower bounds of If (for a large class of arithmetic functions f ) lower bounds for the “Selberg integral” of f , say Jf (both these integrals give informations about f in almo...