Related papers: An exponential estimate for the square partial sum…
It is proved a $BMO$-estimation for quadratic partial sums of two-dimensional Fourier series from which it is derived an almost everywhere exponential summability of quadratic partial sums of double Fourier series.
In this article, we obtain certain estimate for the shifted convolution sum involving the Fourier coefficients of half-integral weight cusp forms.
Let $A$ be a subset of $\mathbb{Z} / N\mathbb{Z}$ and let $\mathcal{R}$ be the set of large Fourier coefficients of $A$. Properties of $\mathcal{R}$ have been studied in works of M.-- C. Chang, B. Green and the author. In the paper we…
In this paper we study the a.e. exponential strong summability problem for the rectangular partial sums of double trigonometric Fourier series of the functions from $L\log L$ .
The main objective of this article is to study the exponential sums associated to Fourier coefficients of modular forms supported at numbers having a fixed set of prime factors. This is achieved by establishing an improvement on…
We estimate the mean square of a short exponential sum involving Fourier coefficients of a cusp form with a linear twist, a smooth weight function, and a relatively short averaging interval.
The partial sums of two quartic basic hypergeometric series are investigated by means of the modified Abel lemma on summation by parts. Several summation and transformation formulae are consequently established.
It is proved a BMO-estimation for quadratic partial sums of two-dimensional Walsh-Fourier series from which it is derived an almost everywhere exponential summability of quadratic partial sums of double Walsh-Fourier series.
In this paper, we investigated the Fourier partial sums with respect to general orthonormal systems when the function $f$ belongs to some differentiable class of functions
In the paper we prove a new upper bound for Heilbronn's exponential sum and obtain some applications of our result to distribution of Fermat quotients.
We investigate exponential sums over singular binary quartic forms, proving an explicit formula for the finite field Fourier transform of this set. Our formula shares much in common with analogous formulas proved previously for other vector…
In this paper we investigate some convergence and divergence properties of the logarithmic means of quadratical partial sums of double Fourier series of functions in the measure and in the $L$ Lebesgue norm.
We present a new single sum series evaluation of Moll's quartic integral and present two new generalizations
New sufficient conditions for representation of a function of several variables as an absolutely convergent Fourier integral are obtained in the paper.
In this paper, we obtain formulas for the number of representations of positive integers as sums of arbitrarily many squares (and other polygonal numbers) with a certain natural weighting. The resulting weighted sums give Fourier…
The main aim of this paper is to investigate the quadratical partial sums of the two-dimensional Walsh-Fourier series.
In this note, we presented a new decomposition of elements of finite fields of even order and illustrated that it is an effective tool in evaluation of some specific exponential sums over finite fields, the explicit value of some…
We calculate the Fourier transform of a spherically symmetric exponential function. Our evaluation is much simpler than the known one. We use the polar coordinates and reduce the Fourier transform to the integral of a rational function of…
The purpose of the article is to estimate the mean square of a squareroot length exponential sum of Fourier coefficients of a holomorphic cusp form.
We examine a family of three-dimensional exponential sums with monomials and provide estimates which are in some instances sharper than those stemming from approaches entailing the use of existing bounds pertaining to analogous sums.