We give a precise determination of the algebraicity critical values L -functions associated to Siegel modular forms half-integral weight and arbitrary degree. generalise improve on similar results for integral-weight case by adapting Rankin-Selberg method this setting, with aid Shimura's theory recent work Bouganis. An essential ingredient is proof new analogue Garrett's conjecture Klingen Eise...

a topoframe, denoted by $l_{ tau}$,  is a pair $(l, tau)$ consisting of a frame $l$ and a subframe $ tau $ all of whose elements are complementary elements in$l$. in this paper, we define and study the notions of a$tau $-real-continuous function on a frame $l$ and the set of realcontinuous functions $mathcal{r}l_tau $ as an $f$-ring.we show that $mathcal{r}l_{ tau}$is actually a generalization ...

Hardy conjectured that there exists an L-function whose inverse is not asymptotic to any L-function. We show that this is true of the L-function log(logx)log(log(logx)).

There are two kinds of L-functions, and they will be described below: motivic L-functions which generalize the Artin L-functions and are defined purely arithmetically, and automorphic L-functions, defined by data which are largely transcendental. Within the automorphic L-functions a special class can be singled out, the class of standard L-functions, which generalize the Hecke L-functions and f...

Symmetrical patterns exist in the nature of inequalities, which play a basic role theoretical and applied mathematics. In several studies, inequalities present accurate approximations functions based on their symmetry properties. paper, we prove completely monotonic (CM) property some involving function Δ(l)=ψ″(l)+ψ′(l)2 hence deduce new double inequality for it. Additionally, study CM degree ψ...

A method for calculating Dirichlet L-series is presented along with the theory of residue class characters and their automatic generation. Tables are given of zeros of Lseries for moduli S 24.

In 1972 H. L. Montgomery announced a remarkable connection between the distribution of the zeros of the Riemann zeta-function and the distribution of eigenvalues of large random Hermitian matrices. Since then a number of startling developments have occurred making this connection more profound. In particular, random matrix theory has been found to be an extremely useful predictive tool in the t...