On Certain Sum Involving Quadratic Residue

Kai An Sim and Kok Bin Wong
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Kai An Sim: School of Mathematical Sciences, Sunway University, Petaling Jaya 47500, Malaysia
Kok Bin Wong: Institute of Mathematical Sciences, Universiti Malaya, Kuala Lumpur 50603, Malaysia

Mathematics, 2022, vol. 10, issue 12, 1-14

Abstract: Let p be a prime and F p be the set of integers modulo p . Let χ p be a function defined on F p such that χ p ( 0 ) = 0 and for a ∈ F p \ { 0 } , set χ p ( a ) = 1 if a is a quadratic residue modulo p and χ p ( a ) = − 1 if a is a quadratic non-residue modulo p . Note that χ p ( a ) = a p is indeed the Legendre symbol. The image of χ p in the set of real numbers. In this paper, we consider the following sum ∑ x ∈ F p χ p ( ( x − a 1 ) ( x − a 2 ) … ( x − a t ) ) where a 1 , a 2 , … , a t are distinct elements in F p .

Keywords: sumset; quadratic residue (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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