Related papers: Sums over Vanishing Determinants
A method for computing integrals of polynomial functions on compact symmetric spaces is given. Those integrals are expressed as sums of functions on symmetric groups.
We study the symmetry in short intervals of arithmetic functions with non-negative exponential sums.
A conjecture is given that, if true, could lead to an algorithm for computing definite sums of rational functions.
The summation arithmetic functions with asymptotically independent summands are studied in the paper. We prove statements about the condition under which the summation arithmetic functions have asymptotically independent summands. It is…
Following an idea due to Euler, we evaluate the alternating sums of powers of consrcutive integers.
To each associative unitary finite-dimensional algebra over a normal base, we associative a canonical multiplicative function called its determinant. We give various properties of this construction, as well as applications to the topology…
We use the periodicity properties of generalized Gauss sums to factor numbers. Moreover, we derive rules for finding the factors and illustrate this factorization scheme for various examples. This algorithm relies solely on interference and…
The dominant theme of this thesis is that random matrix valued analytic functions, generalizing both random matrices and random analytic functions, for many purposes can (and perhaps should) be effectively studied in that level of…
In this paper, we introduce an analog of Gauss sums over function fields in positive characteristic. We establish several fundamental properties, including reflection formula, Stickelberger's theorem, and Hasse-Davenport relations. In…
We study multiplicative nested sums, which are generalizations of harmonic sums, and provide a calculation through multiplication of index matrices. Special cases interpret the index matrices as stochastic transition matrices of random…
Two inequalities involving the Euler totient function and the sum of the $k$-th powers of the divisors of balancing numbers are explored.
We prove recursive formulas for sums of squares and sums of triangular numbers in terms of sums of divisors functions and we give a variety of consequences of these formulas. Intermediate applications include statements about positivity of…
We develop a theoretical study of non-terminating hypergeometric summations with one free parameter. Composing various methods in complex and asymptotic analysis, geometry and arithmetic of certain transcendental curves and rational…
This note gives a few rapidly convergent series representations of the sums of divisors functions. These series have various applications such as exact evaluations of some power series, computing estimates and proving the existence results…
Many results have been established that show how arithmetic conditions on conjugacy class sizes affect group structure. A conjugacy class in $G$ is called vanishing if there exists some irreducible character of $G$ which evaluates to zero…
We study projective functions. We prove that projective functions generalise lower and upper-semianalytic ones while being stable by composition and difference. We show that the class of projective functions is closed under sums,…
We propose results of the investigation of properties of the random sums of random variables. We consider the case, where the number of summands is the first moment of an event occurrence. An integral equation is presented that determines…
Estimation is the computational task of recovering a hidden parameter $x$ associated with a distribution $D_x$, given a measurement $y$ sampled from the distribution. High dimensional estimation problems arise naturally in statistics,…
We study groups, exponential groups and ordered groups equipped with valuations. We investigate algebraic and topological features of such valued structures, and apply our findings in order to solve regular equations over groups using…
The main purpose of this article is to study higher power mean values of generalized quadratic Gauss sums using estimates for character sums, analytic method and algebraic geometric methods. In this article, we prove two conjectures which…