کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
5772646 | 1630633 | 2017 | 34 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
The p-adic valuations of Weil sums of binomials
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
We investigate the p-adic valuation of Weil sums of the form WF,d(a)=âxâFÏ(xdâax), where F is a finite field of characteristic p, Ï is the canonical additive character of F, the exponent d is relatively prime to |FÃ|, and a is an element of F. Such sums often arise in arithmetical calculations and also have applications in information theory. For each F and d one would like to know VF,d, the minimum p-adic valuation of WF,d(a) as a runs through the elements of F. We exclude exponents d that are congruent to a power of p modulo |FÃ| (degenerate d), which yield trivial Weil sums. We prove that VF,dâ¤(2/3)[F:Fp] for any F and any nondegenerate d, and prove that this bound is actually reached in infinitely many fields F. We also prove some stronger bounds that apply when [F:Fp] is a power of 2 or when d is not congruent to 1 modulo pâ1, and show that each of these bounds is reached for infinitely many F.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Number Theory - Volume 181, December 2017, Pages 1-26
Journal: Journal of Number Theory - Volume 181, December 2017, Pages 1-26
نویسندگان
Daniel J. Katz, Philippe Langevin, Sangman Lee, Yakov Sapozhnikov,