On a generalization of Polya inequality and some of its statistical implications

William M.Y. Goh

doi:10.1016/S0377-0427(01)00459-9

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On a generalization of Polya inequality and some of its statistical implications

Journal article

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On a generalization of Polya inequality and some of its statistical implications

William M.Y. Goh

Journal of computational and applied mathematics, v 142(1)

2002

DOI: https://doi.org/10.1016/S0377-0427(01)00459-9

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Abstract

Character

Distribution

Gauss sum

Kloosterman sum

Legendre symbol

Quadratic residue

Riemann hypothesis on finite fields

Let p be a prime and χ a nonprincipal character mod p . Let 1⩽ m⩽ p and l an integer so that p∤l. Then, we have |∑ a=0 m−1 χ(a)χ(a+l)|⩽3 p ln p . The proof makes use of estimation on Kloosterman sum via the Riemann hypothesis on finite fields. As simple consequence of the theorem we obtain a uniform distribution of consecutive quadratic residues mod p .

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Title: On a generalization of Polya inequality and some of its statistical implications
Creators: William M.Y. Goh - Drexel University
Publication Details: Journal of computational and applied mathematics, v 142(1)
Publisher: Elsevier
Resource Type: Journal article
Language: English
Academic Unit: [Retired Faculty]
Web of Science ID: WOS:000175323400006
Scopus ID: 2-s2.0-0036566403
Other Identifier: 991019167455304721

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Web of Science research areas: Mathematics, Applied

On a generalization of Polya inequality and some of its statistical implications

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