Jacquet and Langlands (1970) showed that every infinite dimensional, irreducible, admissible representation of GL(2,Qp) has a unique Kirillov model, i.e. is isomorphic to a representation (π,K), where the space K consists ...
If K is a field whose characteristic is not 2, a quaternion algebra over K is a an algebra over the basis [1,i,j,ij] where i and j satisfy the relations: i2=a j2 =b ij=-ji for a,b in K*. It turns out that for general ...
In 1949, Joseph Lehner published some arithmetic congruences of the Fourier coefficients of the modular invariant j. His method involved applying a certain linear operator to determine congruences modulo primes. Then, he ...
The unrestricted partition function p(n) counts the number of ways a positive integer n can be expressed as a sum of positive integers less than or equal n. The number of summands is unrestricted, repetition is allowed ...
The p-adic numbers were first introduced by Kurt Hensel in 1897 in an attempt to carry the techniques of power series methods from complex analysis into number theory. In this thesis we discuss the relationship between ...
The thesis deals with reduction in linear groups and orthogonal groups. Any matrix y in the set of all n by n symmetric positive definite matrices, can be written as the transpose of an invertible matrix g multiplied by ...
L-functions are generalizations of the Riemann zeta function. We define and study L-functions L(s,χ) attached to Hecke characters χ over number fields Q(α). Such functions converge only when Re(s)1 but have an analytic, ...