Related papers: An identity for the Kloosterman sum

In this note, we present two new identities for derangements. As a corollary, we have a combinatorial proof of the irreducibility of the standard representation of symmetric groups.

We obtain statistical results on the possible distribution of all partial sums of a Kloosterman sum modulo a prime, by computing explicitly the support of the limiting random Fourier series of our earlier functional limit theorem for…

We give combinatorial proofs for some identities involving binomial sums that have no closed form.

We give an alternative proof of a formula that generalizes Hermite's identity. Instead involving modular arithmetic, our short proof relies on the Fourier-type expansion for the floor function and on a trigonometric formula.

We consider the distribution of the polygonal paths joining partial sums of classical Kloosterman sums, as their parameter varies modulo a prime tending to infinity. Using independence of Kloosterman sheaves, we prove convergence in the…

The aim of this short note is to show how can be derived from the properties of fundamental interpolation polynomials some nice identities.

We consider the known functional identity on the Weierstrass sigma function. A complete classification of odd entire functions which satisfy the same identity is obtained.

Let $\mathcal{K}(a)$ denote the Kloosterman sum on the finite field of order $2^n$. We give a simple characterization of $\mathcal{K}(a)$ modulo 16, in terms of the trace of $a$ and one other function. We also give a characterization of…

This purpose of this paper is to note an interesting identity derived from an integral in Gradshteyn and Ryzhik using techniques from George Boros'(deceased) Ph.D thesis. The idenity equates a sum to a product by evaluating an integral in…

In this note we prove two extensions of the Sury's identity.

Utilizing spectral residues of parameterized, recursively defined sequences, we develop a general method for generating identities of composition sums. Specific results are obtained by focusing on coefficient sequences of solutions of first…

We bound Kloosterman-like sums of the shape \[ \sum_{n=1}^N \exp(2\pi i (x \lfloor f(n)\rfloor+ y \lfloor f(n)\rfloor^{-1})/p), \] with integers parts of a real-valued, twice-differentiable function $f$ is satisfying a certain limit…

A family of general integral identities is derived and several applications of physical interest are presented

We develop a new method for studying sums of Kloosterman sums related to the spectral exponential sum. As a corollary, we obtain a new proof of the estimate of Soundararajan and Young for the error term in the prime geodesic theorem.

The main aim of the present paper is to represent an exact and simple proof for FLT by using properties of the algebra identities and linear algebra.

We present a new proof to a general result due to Kestelman. Our proof differs completely from the other proofs we know and we hope that readers will find it clearer. We also include a quite exhaustive bibliographical analysis on related…

We obtain the estimate of incomplete Kloosterman sum to powerful modulus $q$. The length $N$ of the sum lies in the interval $e^{c(\log{q})^{2/3}}\le N\le \sqrt{q}$.

We present a simple iteration for the Lebesgue identity on partitions, which leads to a refinement involving the alternating sums of partitions.

An identity is proved connecting two finite sums of inverse tangents. This identity is discretized version of Jacobi's imaginary transformation for the modular angle from the theory of elliptic functions. Some other related identities are…

We prove a number of new Rogers-Ramanujan type identities involving double, triple and quadruple sums. They were discovered after an extensive search using Maple. The main idea of proofs is to reduce them to some known identities in the…