A new formulation of the law of octic reciprocity for primes =+-3 (mod 8) and its consequences.
A new method of estimation of trigonometrical sums.
A note on a multiplicative hybrid problem
A note on a product formula for the cubic Gauss sum
A note on a result of Bateman and Chowla
A note on arithmetic Diophantine series
We consider an asymptotic analysis for series related to the work of Hardy and Littlewood (1923) on Diophantine approximation, as well as Davenport. In particular, we expand on ideas from some previous work on arithmetic series and the RH. To accomplish this, Mellin inversion is applied to certain infinite series over arithmetic functions to apply Cauchy's residue theorem, and then the remainder of terms is estimated according to the assumption of the RH. In the last section, we use simple properties...
A note on character sums over finite fields.
A note on exponential sums.
A Note on prime k-th power nonresidues.
A note on signs of Kloosterman sums
We prove that the sign of Kloosterman sums changes infinitely often as runs through the square-free numbers with at most prime factors. This improves on a previous result by Sivak-Fischler who obtained 18 instead of 15. Our improvement comes from introducing an elementary inequality which gives lower and upper bounds for the dot product of two sequences whose individual distributions are known.
A note on the Dirichlet characters of polynomials
A note on the distribution of angles associated to indefinite integral binary quadratic forms
To each indefinite integral binary quadratic form , we may associate the geodesic in through the roots of quadratic equation . In this paper we study the asymptotic distribution (as discriminant tends to infinity) of the angles between these geodesics and one fixed vertical geodesic which intersects all of them.
A note on the mean value of the general Kloosterman sums
The main purpose of this paper is to use the analytic method to study the calculating problem of the general Kloosterman sums, and give an exact calculating formula for it.
A note on the zeros of exponential polynomials
A notion of diaphony based on p-adic arithmetic
A problem concerning a character sum.
A problem on semicubical powers
A projective invariant comparing rings of integers in wildly ramified extensions.
A purely analytical lower bound for
We give a simple proof of when is an odd primitiv quadratic Dirichlet character of conductor . In particular we do not use the Dirichlet class-number formula.
A question of the distribution of points on a curve over a finite field.