کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4583331 1333895 2008 10 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Bilinear character sums over elliptic curves
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
Bilinear character sums over elliptic curves
چکیده انگلیسی

Let E be an elliptic curve over a finite field FqFq of q elements given by an affine Weierstraß equation. Let ⊕ denote the group operation in the Abelian group of points on E. We also use x(P)x(P) to denote the x  -component of a point P=(x(P),y(P))∈EP=(x(P),y(P))∈E.We estimate character sumsWρ,ϑ(ψ,U,V)=∑U∈U∑V∈Vρ(U)ϑ(V)ψ(x(U⊕V)), where UU and VV are arbitrary sets of FqFq-rational points on E, ψ   is a nontrivial additive character of FqFq and ρ(U)ρ(U) and ϑ(V)ϑ(V) are arbitrary bounded complex functions supported on UU and VV, respectively. Our bound of sums Wρ,ϑ(ψ,U,V)Wρ,ϑ(ψ,U,V) is nontrivial whenever#U>q1/2+εand#V>qε for some fixed ε>0ε>0. We also give various applications of this bound.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Finite Fields and Their Applications - Volume 14, Issue 1, January 2008, Pages 132–141
نویسندگان
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