کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
11033145 | 1630349 | 2018 | 10 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Carlitz-Wan conjecture for permutation polynomials and Weill bound for curves over finite fields
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
The Carlitz-Wan conjecture, which is now a theorem, asserts that for any positive integer n, there is a constant Cn such that if q is any prime power >Cn with GCD(n,qâ1)>1, then there is no permutation polynomial of degree n over the finite field with q elements. From the work of von zur Gathen, it is known that one can take Cn=n4. On the other hand, a conjecture of Mullen, which asserts essentially that one can take Cn=n(nâ2) has been shown to be false. In this paper, we use a precise version of Weil bound for the number of points of affine algebraic curves over finite fields to obtain a refinement of the result of von zur Gathen where n4 is replaced by a sharper bound. As a corollary, we show that Mullen's conjecture holds in the affirmative if n(nâ2) is replaced by n2(nâ2)2.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Finite Fields and Their Applications - Volume 54, November 2018, Pages 366-375
Journal: Finite Fields and Their Applications - Volume 54, November 2018, Pages 366-375
نویسندگان
Jasbir S. Chahal, Sudhir R. Ghorpade,