Let B/Q be an indefinite quaternion algebra of discriminant D (we allow the case of D = 1, i.e., B ∼= M2(Q)) and ON a level N Eichler order in B. By taking Γ(ON ) = Γ(B,ON ) to be the elements of O× of positive reduced norm, we get an arithmetic Fuchsian group and hence a Riemann surface ON\H. So as not to prejudice matters, let us temporarily denote the Shimura curve associated to any quaterni...

A necessary and sufficient condition for a central simple algebra with involution over a field of characteristic two to be decomposable as a tensor product of quaternion algebras with involution, in terms of its Frobenius subalgebras, is given. It is also proved that a bilinear Pfister form, recently introduced by A. Dolphin, can classify totally decomposable central simple algebras of orthogon...

In this paper, we consider the relation between the simplest types of arithmetic theta series, those associated to the cycles on the moduli space C of elliptic curves with CM by the ring of integers Ok in an imaginary quadratic field k, on the one hand, and those associated to cycles on the arithmetic surface M parametrizing 2-dimensional abelian varieties with an action of the maximal order OB...

Let B be a quaternion algebra over number field K : Assume that B satisfies the Eichler condition (i.e., there is at least one archimedean place which is unramified in B). Let O be an order in a quadratic extension L of K: The Eichler orders of B which admit an embedding of O are determined. This is a generalization of Chinburg and Friedman’s embedding theorem for maximal orders. r 2004 Elsevie...

We obtain a formula relating the Fourier coefficients of a modular form of half-integral weight (that is constructed as a theta lift from an indefinite quaternion algebra B over Q) to the special values of L-functions. This formula has applications to proving the nonvanishing of a certain explicit theta lift and to an explicit version of the Rallis inner product formula for the dual pair (S̃L2, ...

We study the possible weights of an irreducible 2-dimensional mod p representation of Gal(F/F ) which is modular in the sense of that it comes from an automorphic form on a definite quaternion algebra with centre F which is ramified at all places dividing p, where F is a totally real field. In most cases we determine the precise list of possible weights; in the remaining cases we determine the ...

Modern techniques treat color images as separate monochrome images for processing. Partly, because there is no straightforward generalization of linear filters available for color. However the algorithms yield more accurate results when the correlation among color bands are exploited which shows fundamental difference to process the color images. Earlier work[8] reported the transformation of t...

We describe a process for defining and computing a fundamental domain in the upper half plane H of a Shimura curve X 0 (N) associated to an order in a quaternion algebra A/Q. A fundamental domain for X 0 (N) realizes a finite presentation of the quaternion unit group, modulo units of its center. We give explicit examples of domains for the curves X 0 (1), X 0 (1), and X 35 0 (1). The first exam...

The density conjecture of Katz and Sarnak predicts that, for natural families L-functions, the distribution zeros lying near real axis is governed by a group symmetry. In case universal family automorphic forms on totally definite quaternion algebra, we determine associated restricted class test functions in analytic conductor aspect. particular it leads to non-trivial results densities non-van...