Related papers: Classes of forms Witt equivalent to a second trace…

The aim of this paper is twofold: on one hand we study the invariants of traces of quadratic forms over a finite field of characteristic two. On the other hand, we give results about the zeta functions of certain curves studied by van der…

In this paper we classify curves of genus two over a perfect field k of characteristic two. We find rational models of curves with a given arithmetic structure for the ramification divisor and we give necessary and sufficient conditions for…

The conjugacy class of a generic unimodular 2 by 2 complex matrix is determined by its trace, which may be an arbitrary complex number. In the nineteenth century, it was known that a generic pair (X,Y) of such pairs is determined up to…

We consider a class of linear ODEs of second order with variable coefficients and construct its Lie algebra of Lie group of equivalence transformations. Further we find invariants and differential invariants of this Lie algebra and by using…

For any finite dimensional C^*-algebra A with a trace vector \vec s whose entries are rational numbers, we give an endomorphism \Phi of the hyperfinite II_1 factor R such that: for all k \in \mathbb {N}, \Phi^k (R)' \cap R= \otimes^k A. The…

We give an upper bound for the norm of the determinant of additively indecomposable, totally positive definite quadratic forms defined over the ring of integers of totally real number fields. We apply these results to find lower and upper…

Let $\varphi$ and $\psi$ be quadratic forms over a field $K$ of characteristic different from 2. In this paper, we give a criterion for isotropy of $\varphi$ over the function field of $\psi$ in terms of representations and we apply it to…

Cubic surfaces in characteristic two are investigated from the point of view of prime characteristic commutative algebra. In particular, we prove that, the non-Frobenius split cubic surfaces form a linear subspace of codimension four in the…

We show that many important natural science models in their mathematical formulation can be reduced to non-strictly hyperbolic systems of the same kind. This allows the same methods to be applied to them so that some essential results…

We provide a clarification of the classification of two-dimensional algebras over an arbitrary base field. Using this clarification, we determine the number of non-isomorphic two-dimensional algebras over a finite field.

Jagy and Kaplansky exhibited a table of 68 pairs of positive definite binary quadratic forms that represent the same odd primes and conjectured that this list is complete outside of "trivial" pairs. In this article, we find all pairs of…

Let E/Q be a real quadratic field and pi_0 a cuspidal, irreducible, automorphic representation of GL(2,A_E) with trivial central character and infinity type (2,2n+2) for some non-negative integer n. We show that there exists a non-zero…

We investigate the graded Lie algebras of Cartan type $W$, $S$ and $H$ in characteristic 2 and determine their simple constituents and some exceptional isomorphisms between them. We also consider the graded Lie algebras of Cartan type $K$…

The spin analogues of several classical concepts and results for Hecke algebras are established. A Frobenius type formula is obtained for irreducible characters of the Hecke-Clifford algebra. A precise characterization of the trace…

We prove the Hasse principle and weak approximation for varieties defined over number fields by the nonsingular intersection of pairs of quadratic forms in 8 variables. The argument develops work of Colliot-Thelene, Sansuc and…

Let $\psi$ and $F$ be positive definite forms with integral coefficients of equal degree. Using the circle method, we establish an asymptotic formula for the number of identical representations of $\psi$ by $F$, provided $\psi$ is…

We show that a non-hyperbolic orthogonal involution on a central simple algebra over a field of characteristic different from 2 remains non-hyperbolic over some splitting field of the algebra.

We exhibit an extension of the category of class two nilpotent groups. It has the same objects but, unlike the latter, its morphisms are closed under pointwise addition of maps. At the same time the class of its morphisms is much smaller…

We prove an analogue of Selberg's trace formula for a delta potential on a hyperbolic surface of finite volume. For simplicity we restrict ourselves to surfaces with at most one cusp, but our methods can easily be extended to any number of…

We consider generalized quadratic forms over real quadratic number fields and prove, under a natural positive-definiteness condition, that a generalized quadratic form can only be universal if it contains a quadratic subform that is…