Related papers: Closed Forms Evaluations Of Some Exponential Sums
In this paper, we completely determine the slopes and weights of the L-functions of an important class of exponential sums arising from analytic number theory. Our main tools include Adolphson-Sperber's work on toric exponential sums and…
This paper develops an approach to the evaluation of quadratic Euler sums that involve harmonic numbers. The approach is based on simple integral computations of polyloga- rithms. By using the approach, we establish some relations between…
We study three classes of combinatorial sums involving central binomial coefficients and harmonic numbers, odd harmonic numbers, and even indexed harmonic numbers, respectively. In each case we use summation by parts to derive recursive…
We examine exponential sums of the form $\sum_{n \le X} w(n) e^{2\pi i\alpha n^k}$, for $k=1,2$, where $\alpha$ satisfies a generalized Diophantine approximation and where $w$ are different arithmetic functions that might be multiplicative,…
Using matrix inversion and determinant evaluation techniques we prove several summation and transformation formulas for terminating, balanced, very-well-poised, elliptic hypergeometric series.
This article presents a comprehensive overview and supplement to recent developments in second-order elliptic partial differential equations formulated in double divergence form, along with an exploration of their parabolic counterparts.
This is a survey of old and new problems and results in additive number theory.
A survey is given on mathematical structures which emerge in multi-loop Feynman diagrams. These are multiply nested sums, and, associated to them by an inverse Mellin transform, specific iterated integrals. Both classes lead to sets of…
Recent progress in analytical calculation of the multiple [inverse, binomial, harmonic] sums, related with epsilon-expansion of the hypergeometric function of one variable are discussed.
This paper introduces a symbolic calculus-based approach for deriving closed-form expressions for the sums of arithmetic sequences. The method extends beyond constant-difference sequences to those with polynomially increasing steps,…
The variation distance closure of an exponential family with a convex set of canonical parameters is described, assuming no regularity conditions. The tools are the concepts of convex core of a measure and extension of an exponential…
We explore several variations on the recently discovered phenomena of murmurations for elliptic curves and modular forms.
This article is a survey of the exponential polynomials (also called single-variable Bell polynomials) from the point of view of Analysis. Some new properties are included and several Analysis-related applications are mentioned.
In this article we present ways to evaluate certain sums, products and continued fractions using tools from the theory of elliptic functions. The specific results appear to be new, although similar ones can be found in the leterature; in…
We obtain some optimal estimates for multilinear forms on $\ell _{p}$ spaces.
We characterize the extendibility of the normal curvature on frontals and we give a representation formula of this type of frontals. Also we give representation formulas for wavefronts on all types of singularities and others sub classes of…
Generic Newton polygons for L-functions of exponential sums associated to Laurent polynomials in one variable are determined. The corresponding Hasse polynomials are also determined.
We present several closed-form expressions of useful mass distributions. These include the potentials and accelerations of circular rings and arcs, the potentials of uniform density rings and arcs at arbitrary eccentricities, and the…
We obtain upper bounds for the fourth and higher moments of short exponential sums involving Fourier coefficients of holomorphic cusp forms twisted by rational additive twists with small denominators.
The main purpose of the present article is to give some new Hilbert's sum type inequalities, which in special cases yield the classical Hilbert's inequalities. Our results provide some new estimates to these types of inequalities.