Results 61 to 70 of about 165,955 (179)

On the generalized exponential sums and their fourth power mean

Open Mathematics
The main purpose of this article is to study the calculating problem of the fourth power mean of the two-term exponential sums and provide an accurate calculating formula for utilizing analytical methods and character sums’ properties. In the meantime, a
Liu Wencong, Ning Shushu
doaj   +1 more source

The Weight Distributions of a Class of Cyclic Codes with Three Nonzeros over 𝔽3

Journal of Applied Mathematics, 2014
Cyclic codes have efficient encoding and decoding algorithms. The decoding error probability and the undetected error probability are usually bounded by or given from the weight distributions of the codes.
Xiaogang Liu, Yuan Luo
doaj   +1 more source

A Novel Integral Equation for the Riemann Zeta Function and Large t-Asymptotics

Mathematics, 2019
Based on the new approach to Lindelöf hypothesis recently introduced by one of the authors, we first derive a novel integral equation for the square of the absolute value of the Riemann zeta function.
Konstantinos Kalimeris, Athanassios S. Fokas   +1 more
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A Generalized Equilibrium Transform with Application to Error Bounds in the Rényi Theorem with No Support Constraints

Mathematics, 2020
We introduce a generalized stationary renewal distribution (also called the equilibrium transform) for arbitrary distributions with finite nonzero first moment and study its properties.
Irina Shevtsova, Mikhail Tselishchev
doaj   +1 more source

An exact renormalization formula for Gaussian exponential sums and applications

, 2009
In the present paper, we derive a renormalization formula "\`a la Hardy-Littlewood" for the Gaussian exponential sums with an exact formula for the remainder term.
Fedotov, Alexander, Klopp, Frédéric
core   +1 more source

Exponential Sums and Lattice Points [PDF]

Proceedings of the London Mathematical Society, 1990
The area A inside a simple closed curve C can be estimated graphically by drawing a square lattice of sides 1/M. The number of lattice points inside C is approximately \(AM^ 2\). If C has continuous nonzero radius of curvature, the number of lattice points is accurate to order of magnitude at most \(M^{\alpha}\) for any \(\alpha >2/3\). We show that if
openaire   +2 more sources

Generating Functions for New Families of Combinatorial Numbers and Polynomials: Approach to Poisson–Charlier Polynomials and Probability Distribution Function

Axioms, 2019
The aim of this paper is to construct generating functions for new families of combinatorial numbers and polynomials. By using these generating functions with their functional and differential equations, we not only investigate properties of these new ...
Irem Kucukoglu, Burcin Simsek, Yilmaz Simsek   +2 more
doaj   +1 more source

Mordell’s exponential sum estimate revisited [PDF]

Journal of the American Mathematical Society, 2005
The aim of this paper is to extend recent work of S. Konyagin and the author on Gauss sum estimates for large degree to the case of ‘sparse’ polynomials. In this context we do obtain a nearly optimal result, improving on the works of Mordell and of Cochrane and Pinner.
openaire   +2 more sources

IGUSA’S CONJECTURE FOR EXPONENTIAL SUMS: OPTIMAL ESTIMATES FOR NONRATIONAL SINGULARITIES

Forum of Mathematics, Pi, 2019
We prove an upper bound on the log canonical threshold of a hypersurface that satisfies a certain power condition and use it to prove several generalizations of Igusa’s conjecture on exponential sums, with the log canonical threshold in the exponent of ...
RAF CLUCKERS, MIRCEA MUSTAŢĂ, KIEN HUU NGUYEN   +2 more
doaj   +1 more source

On the Exponential Inequality for Weighted Sums of a Class of Linearly Negative Quadrant Dependent Random Variables

The Scientific World Journal, 2014
The exponential inequality for weighted sums of a class of linearly negative quadrant dependent random variables is established, which extends and improves the corresponding ones obtained by Ko et al. (2007) and Jabbari et al. (2009).
Guodong Xing, Shanchao Yang
doaj   +1 more source