Contents 0 Introduction 1 1 Preliminaries 4 2 p-power twists 7 3 Quadratic twists 13 4 Generation of coeecient elds by ratios of L-values 20 5 p-adic L-functions 22 6 Forms of half integral weight 25 Bibliography 28 0 Introduction Let f be a normalized holomorphic newform (deened on the upper half plane H) of level N, weight 2k and trivial character. It is given by a Fourier expansion f(z) = P ...

We investigate a few types of generalizations of the Hurwitz zeta function, written Z(s, a) in this abstract, where s is a complex variable and a is a parameter in the domain that depends on the type. In the easiest case we take a ∈ R, and one of our main results is that Z(−m, a) is a constant times Em(a) for 0 ≤ m ∈ Z, where Em is the generalized Euler polynomial of degree n. In another case, ...

A careful investigation of different corrections to binding energies of electrons in almost critical fields is performed. We investigate quantitatively the influence of the nuclear charge parameters, nuclear mass, degree of ionization on the value of the critical charge of the nucleus. Rather qualitative arguments are given to establish the contribution of the quantumelectrodynamic corrections,...

Let M be a quantizable symplectic manifold acted on by T = (S) in a Hamiltonian fashion and J a moment map for this action. Suppose that the set M of fixed points is discrete and denote by αpj ∈ Z the weights of the isotropy representation at p. By means of the αpj ’s we define a partition Q+, Q− of M . (When r = 1, Q± will be the set of fixed points such that the half of the Morse index of J a...

We denote by Conc L the (∨, 0)-semilattice of all finitely generated congruences of a lattice L. For varieties (i.e., equational classes) V and W of lattices such that V is contained neither in W nor in its dual, and such that every simple member of W contains a prime interval, we prove that there exists a bounded lattice A ∈ V with at most א2 elements such that Conc A is not isomorphic to Conc...

We consider weak and strong survival for branching random walks on multigraphs with bounded degree. We prove that, at the strong critical value, the process dies out locally almost surely. We relate the weak critical value to a geometrical parameter of the multigraph. For a large class of multigraphs (which enlarges the class of quasi-transitive or regular graphs) we prove that, at the weak cri...