Fourier expansion of Arakawa lifting II: Relation with central L-values

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...

Lifting Imprecise Values

The article presents a conceptual framework for computations with imprecise values. Typically, the treatment of imprecise values differs from the treatment of precise values. While precise computations use a single number to characterize a value, computations with imprecise values must deal with several numbers for each value. This results in significant changes in the program code because valu...

Arithmetic theta lifting and L-derivatives for unitary groups, II

Relation lifting, a survey

We survey work in category theory and coalgebra on how to extend a functor from maps to relations. This relation lifting has a universal property, which is presented in some detail and guides us to generalisations to monotone and many-valued relations. As applications, it is shown how different notions of bisimulation, simulation and modal logics do arise.