Related papers: Correlations of representation functions of binary…

The so-called polynomial equations play an important role both in algebra and in the theory of functional equations. If the unknown functions in the equation are additive, relatively many results are known. However, even in this case, there…

In this paper, we investigate three-term linear relations among theta series of positive-definite integral binary quadratic forms. We extend Schiemann's methods to characterize all possible three-term linear relations among theta series of…

In this paper, we work out some explicit formulae for double nonlinear Euler sums involving harmonic numbers and alternating harmonic numbers. As applications of these formulae, we give new closed form representations of several quadratic…

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 derive "numerical" criteria for the existence of embeddings of representations of finite dimensional algebras.

In the previous article we introduced the new concept of mixed representations of quivers and described the generators of their algebras of invariants. In this article we describe the defining relations of these algebras. Some applications…

We offer some partition functions related to ternary quadratic forms, and note on their upper bounds and related properties. We offer these results as an application of a simple method related to conjugate Bailey pairs presented in a prior…

For a broad class of Frechet-Lie supergroups we prove that there exists a correspondence between positive definite smooth superfunctions and matrix coefficients of unitary representations. We also give a characterization of linear…

A strong consequence of quadratic forms becoming hyperbolic over the function field of a form is established. This result is invoked to obtain a new characterisation of hyperbolicity over function fields, and to recover a number of…

We provide a geometric characterisation of binary sextics with vanishing quadratic invariant.

In this paper, with the help of trinomial coefficients we study some arithmetic properties of certain determiants involving reciprocals of binary quadratic forms over finite fields.

Suppose $k$ is a positive integer. In this work, we establish formulas for for the number of representations of integers by the quadratic forms $$ x_{1}^{2}+\cdots+x_{k}^{2}+l\left(x_{k+1}^{2}+\cdots+x_{2k}^{2}\right) $$ for $l\in\{2,4\}$.

Both a general and a diagonal u-invariant for forms of higher degree are defined, generalizing the u-invariant of quadratic forms. Both old and new results on these invariants are collected.

An integral quadratic form is called strictly $n$-regular if it primitively represents all quadratic forms in $n$ variables that are primitively represented by its genus. For any $n \geq 2$, it will be shown that there are only finitely…

We develop new closed form representations of sums of (n + {\alpha})th shifted harmonic numbers and reciprocal binomial coefficients in terms of {\alpha}th shifted harmonic numbers. Some interesting new consequences and illustrative…

This work deals with the conformal transformations in six-dimensional spinorial formalism. Several conformally invariant equations are obtained and their geometrical interpretation are worked out. Finally, the integrability conditions for…

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…

In this article we consider certain types of weighted generalized functions associated with nondegenerate quadratic forms. Such functions and their derivatives are used for constructing fundamental solutions of iterated ultra-hyperbolic…

In this paper we study representations of conformal nets associated with positive definite even lattices and their orbifolds with respect to isometries of the lattices. Using previous general results on orbifolds, we give a list of all…

We provide a coherent picture of our efforts thus far in extending real algebra and its links to the theory of quadratic forms over ordered fields in the noncommutative direction, using hermitian forms and "ordered" algebras with…