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Explicit evaluation of certain exponential sums of binary quadratic functions

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Xiang-Dong HouAuthors Info & Claims

Finite Fields and Their Applications, Volume 13, Issue 4

Pages 843 - 868

https://doi.org/10.1016/j.ffa.2006.09.009

Published: 01 November 2007 Publication History

Abstract

Let 0<@a"1<...<@a"k be integers and f(x)=@__ __"i"="1^ka"ix^2^^^@a^^^"^^^i^+^1+bx@__ __F"2"^"m[x], a"k<>0. Define S(f,n)=@__ __"x"@__ __"F"""2"""^"""ne(f(x)) where m|n and e(x)=(-1)^T^r^"^F^"^"^"^2^"^"^"^^^"^"^"^n^"^/^"^F^"^"^"^2^(^x^). We establish a relation among S(f,n) for all n with the same 2-adic order. When @n"2(@a"1)=...=@n"2(@a"k), where @n"2 is the 2-adic order function, we are able to compute S(f,n) explicitly for all n with a given f. Moreover, we are able to compute S(ax^2^^^@a^+^1+cx,n) explicitly for all @a>0, a@__ __F"2"^"m, m|n and c@__ __F"2"^"n.

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cover image Finite Fields and Their Applications

Finite Fields and Their Applications Volume 13, Issue 4

November, 2007

401 pages

ISSN:1071-5797

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Elsevier Science Publishers B. V.

Netherlands

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Published: 01 November 2007

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