On certain sum involving quadratic residue
Let p be a prime and F-p be the set of integers modulo p. Let chi(p) be a function defined on F-p such that chi(p)(0) = 0 and for a is an element of F-p\textbackslash{0}, set chi(p)(a) = 1 if a is a quadratic residue modulo p and chi(p)(a)= -1 if a is a quadratic non-residue modulo p. Note that chi(...
保存先:
主要な著者: | , |
---|---|
フォーマット: | 論文 |
出版事項: |
MDPI
2022
|
主題: | |
オンライン・アクセス: | http://eprints.um.edu.my/41968/ |
タグ: |
タグ追加
タグなし, このレコードへの初めてのタグを付けませんか!
|
要約: | Let p be a prime and F-p be the set of integers modulo p. Let chi(p) be a function defined on F-p such that chi(p)(0) = 0 and for a is an element of F-p\textbackslash{0}, set chi(p)(a) = 1 if a is a quadratic residue modulo p and chi(p)(a)= -1 if a is a quadratic non-residue modulo p. Note that chi(p)(a)=(a/p) is indeed the Legendre symbol. The image of chi(p) in the set of real numbers. In this paper, we consider the following sum Sigma(x is an element of Fp)chi(p)((x-a(1))(x-a(2))...(x-a(t))) where a(1),a(2), ...,a(t) are distinct elements in F-p. |
---|