Zeroes of quaternionic modular forms and central L-values

Vector valued hermitian and quaternionic modular forms

Determination of Modular Forms by Twists of Critical L-values

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 ...

Quaternionic Manin symbols, Brandt matrices, and Hilbert modular forms

In this paper, we propose a generalization of the algorithm developed in [4]. Along the way, we also develop a theory of quaternionic M -symbols whose definition bears some resemblance with the classical M -symbols, except for their combinatorial nature. The theory gives a more efficient way to compute Hilbert modular forms over totally fields, especially quadratic fields, and we have illustrat...

Intersections of Higher-weight Cycles over Quaternionic Modular Surfaces and Modular Forms of Nebentypus

In 1976 Hirzebruch and Zagier [6] computed the pairwise intersection multiplicities for a family of algebraic cycles (T£)n(EN in the Hubert modular surface associated to Q(yp), where p is a prime congruent to 1 mod 4, and showed that the generating function for those intersection multiplicities Yln°=oC^m 'T£)e[nr] was an elliptic modular form of weight 2 and Nebentypus for To(p). Shortly afterw...

Congruences for Fourier Coefficients of Half-integral Weight Modular Forms and Special Values of L−functions

Congruences for Fourier coefficients of integer weight modular forms have been the focal point of a number of investigations. In this note we shall exhibit congruences for Fourier coefficients of a slightly different type. Let f(z) = P∞ n=0 a(n)q n be a holomorphic half integer weight modular form with integer coefficients. If ` is prime, then we shall be interested in congruences of the form