Stable averages of central values of Rankin–Selberg L -functions: Some new variants

Central Values of Degree Six L-functions

Let κ′, κ ≥ 3 be two odd integers. Let f (resp. g) be a normalized holomorphic modular form of weight 2κ (resp. κ′ + 1) and level one on the upper half plane h. Assume that they are Hecke eigenforms. Let L(s, Sym g×f) be the completed degree six L-function and we normalize so that s = 1 2 is the center of symmetry. Let 〈−,−〉 be the Petersson inner product, defined using the usual measure on h s...

Computing Central Values of L-functions

How fast can we compute the value of an L-function at the center of the critical strip? We will divide this question into two separate questions while also making it more precise. Fix an elliptic curve E defined over Q and let L(E, s) be its L-series. For each fundamental discriminant D let L(E,D, s) be the L-series of the twist ED of E by the corresponding quadratic character; note that L(E, 1...

Central Values of Hecke L-functions of Cm Number Fields

0. Introduction. It is well known that the zeta function of CM (complex multiplication) abelian varieties can be given in terms of L-functions of associated Hecke characters. In this paper, we prove a formula expressing the central special value of the L-function of certain Hecke characters in terms of theta functions. The formula easily implies that the central value is nonnegative and yields ...

The Cubic Moment of Central Values of Automorphic L-functions

detection of volatile compounds of medicinal plants with some nano-sorbents using modified or new methodologies and investigation of antioxidant activity of their methanolic extracts

in this work, a novel and fast method for direct analysis of volatile compounds (davc) of medicinal plants has been developed by holding a filament from different parts of a plant in the gc injection port. the extraction and analysis of volatile components of a small amount of plant were carried out in one-step without any sample preparation. after optimization of temperature, extraction time a...