Let B be an undefined quaternion algebra over Q. Following the explicit chacterization of some Eichler orders in B given by Hashimoto, we define explicit embeddings of these orders in some local rings of matrices; we describe the two natural inclusions of an Eichler order of leven Nq in an Eichler order of level N . Moreover we provide a basis for a chain of Eichler orders in B and prove result...

Let K be a quadratic extension of Q, B a quaternion algebra over Q and A = B ⊗Q K. Let O be a maximal order in A extending an order in B. The projective norm one group PO1 is shown to be isomorphic to the spinorial kernel group O′(L), for an explicitly determined quadratic Z-lattice L of rank four, in several general situations. In other cases, only the local structures of O and L are given at ...

Abstract Let k be an algebraically closed field of prime characteristic p . $kGe$ a block group algebra finite G , with normal defect P and abelian $p'$ inertial quotient L Then we show that is matrix over quantised version the semidirect product certain subgroup To do this, first examine associated graded algebra, using Jennings–Quillen style theorem. As example, calculate basic nonprincipal i...

Abstract We develop the relationship between quaternionic hyperbolic geometry and arithmetic counting or equidistribution applications, that arises from action of groups on spaces, especially in dimension 2. prove a Mertens formula for rational points over definite quaternion algebra A ${\mathbb{Q}}$ light cone Hermitian forms, as well Neville theorem set Heisenberg groups.

Let K be a totally real algebraic number field and O an order in a quaternion algebra A over K. Assume that the group O1 of units in O with reduced norm equal to 1 is embedded into PSL2(R) as an arithmetic Fuchsian group. It is shown how Ford’s algorithm can be effectively applied in order to determine a fundamental domain of O1 as well as a complete system of generators of O1.

Let X be an arithmetic hyperbolic surface arising from a quaternion division algebra over Q. Let be a Hecke–Maass form on X , and let ` be a geodesic segment. We obtain a power saving over the local bound of Burq, Gérard, and Tzvetkov for the L-norm of restricted to `, by extending the technique of arithmetic amplification developed by Iwaniec and Sarnak. We also improve the local bounds for va...

Let O be a maximal order in a totally indefinite quaternion algebra over a totally real number field. In this note we study the locus QO of quaternionic multiplication byO in the moduli spaceAg of principally polarized abelian varieties of even dimension g with particular emphasis in the two-dimensional case. We describe QO as a union of Atkin-Lehner quotients of Shimura varieties and we comput...

• Vectorspaces over division rings • Matrices, opposite rings • Semi-simple modules and rings • Semi-simple algebras • Reduced trace and norm • Other criteria for simplicity • Involutions • Brauer group of a field • Tensor products of fields • Crossed product construction of simple algebras • Cyclic algebra construction of simple algebras • Quaternion algebras • Examples • Unramified extensions...

. The constants are effectively computable. Proof. Part (a) follows from the fact that the algebraic group GSp2g has dimension 2g +g+1. Part (b) is obvious. Combined with Theorem 1.1 of [Ghi04], Theorem 1 gives Corollary 3 (Algebraic modular forms). Let B/Q be the quaternion algebra ramified at p and ∞. The number of systems of Hecke eigenvalues coming from algebraic modular forms (mod p) of le...