Exponential sums with Catalan numbers and middle binomial coefficients

Moubariz Z. Garaev; Florian Luca; Igor E. Shparlinski

doi:10.1016/S0019-3577(07)80004-8

Exponential sums with Catalan numbers and middle binomial coefficients

Moubariz Z. Garaev^*, Florian Luca, Igor E. Shparlinski

^*Corresponding author for this work

School of Computing

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

We estimate the number of solutions of certain congruences with Catalan numbers and middle binomial coefficients modulo a prime. We use these results to bound double exponential sums with products of two Catalan numbers and two middle binomial coefficients, respectively, which in turn lead us to upper bounds on single exponential sums.

Original language	English
Pages (from-to)	23-37
Number of pages	15
Journal	Indagationes Mathematicae
Volume	18
Issue number	1
DOIs	https://doi.org/10.1016/S0019-3577(07)80004-8
Publication status	Published - 2007

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title = "Exponential sums with Catalan numbers and middle binomial coefficients",

abstract = "We estimate the number of solutions of certain congruences with Catalan numbers and middle binomial coefficients modulo a prime. We use these results to bound double exponential sums with products of two Catalan numbers and two middle binomial coefficients, respectively, which in turn lead us to upper bounds on single exponential sums.",

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T1 - Exponential sums with Catalan numbers and middle binomial coefficients

AU - Garaev, Moubariz Z.

AU - Luca, Florian

AU - Shparlinski, Igor E.

PY - 2007

Y1 - 2007

N2 - We estimate the number of solutions of certain congruences with Catalan numbers and middle binomial coefficients modulo a prime. We use these results to bound double exponential sums with products of two Catalan numbers and two middle binomial coefficients, respectively, which in turn lead us to upper bounds on single exponential sums.

AB - We estimate the number of solutions of certain congruences with Catalan numbers and middle binomial coefficients modulo a prime. We use these results to bound double exponential sums with products of two Catalan numbers and two middle binomial coefficients, respectively, which in turn lead us to upper bounds on single exponential sums.

UR - https://www.scopus.com/pages/publications/34447283071

U2 - 10.1016/S0019-3577(07)80004-8

DO - 10.1016/S0019-3577(07)80004-8

M3 - Article

AN - SCOPUS:34447283071

SN - 0019-3577

VL - 18

SP - 23

EP - 37

JO - Indagationes Mathematicae

JF - Indagationes Mathematicae

IS - 1

ER -

Exponential sums with Catalan numbers and middle binomial coefficients

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