Related papers: On quadratic character sums over quartics
Using a quadratic version of the Bott residue theorem, we give a quadratic refinement of the count of twisted cubic curves on hypersurfaces and complete intersections in a projective space.
In this paper we will give a proof of a certain summation formula for Gamma functions utilizing Gegenbauer polynomials.
In this note, we derive a finite summation formula and an infinite summation formula involving Harmonic numbers of order up to some order by means of several definite integrals
We obtain a new bound on certain double sums of multiplicative characters improving the range of several previous results. This improvement comes from new bounds on the number of collinear triples in finite fields, which is a classical…
We use an elementary argument to prove some finite sums involving expressions of the forms $(q)_n$ and $(a;q)_n$ along with inductive formulas for some sequences.
A number of new terminating series involving $\sin(n^2/k)$ and $\cos(n^2/k)$ are presented and connected to Gauss quadratic sums. Several new closed forms of generic Gauss quadratic sums are obtained and previously known results are…
We obtain a series of lower bounds for the product set of combinatorial cubes, as well as some non--trivial upper estimates for the multiplicative energy of such sets.
We apply a symbolic approach of the general quadratic decomposition of polynomial sequences - presented in a previous article referenced herein - to polynomial sequences fulfilling specific orthogonal conditions towards two given…
We give explicit upper bounds for coefficients of polynomials appearing in Gauss-Kra\"{i}tchik formula for cyclotomic polynomials. We use a certain relation between elementary symmetric polynomials and power sums polynomials.
We extend some results about shifted Schur functions to the general context of shifted Macdonald polynomials. We obtain two explicit formulas for these polynomials: a $q$-integral representation and a combinatorial formula. Our main tool is…
We parametrize quartic commutative algebras over any base ring or scheme (equivalently finite, flat degree four $S$-schemes), with their cubic resolvents, by pairs of ternary quadratic forms over the base. This generalizes Bhargava's…
We derive a general recurrence relation for squares of Fibonacci-like numbers. Various properties are developed, including double binomial summation identites.
In this paper, we apply high level versions of Jacobi's derivative formula to number theory such as quarternary quadratic forms and convolution sums of some arithmetical functions.
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…
The classical quadratic Gauss sum can be thought of as an exponential sum attached to a quadratic form on a cyclic group. We introduce an equivariant version of Gauss sum for arbitrary finite quadratic forms, which is an exponential sum…
We study real quadratic fields $\mathbb{Q}(\sqrt{D})$ such that, for a given rational integer $m$, all $m$-multiples of totally positive integers are sums of squares. We prove quite sharp necessary and sufficient conditions for this to…
We give solutions of a Diophantine equation containing factorials, which can be written as a cubic form, or as a sum of binomial coefficients. We also give some solutions to higher degree forms and relate some solutions to an unsolvable…
In this article, we obtain certain estimate for the shifted convolution sum involving the Fourier coefficients of half-integral weight cusp forms.
Permutation polynomials are an interesting subject of mathematics and have applications in other areas of mathematics and engineering. In this paper, we develop general theorems on permutation polynomials over finite fields. As a…
In this paper, by using the theory of circulant matrices we study some matrices over finite fields which involve the quadratic character and trinomial coefficients.