کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
5771552 | 1630355 | 2017 | 19 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
The k-resultant modulus set problem on algebraic varieties over finite fields
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
![عکس صفحه اول مقاله: The k-resultant modulus set problem on algebraic varieties over finite fields The k-resultant modulus set problem on algebraic varieties over finite fields](/preview/png/5771552.png)
چکیده انگلیسی
We study the k-resultant modulus set problem in the d-dimensional vector space Fqd over the finite field Fq with q elements. Given EâFqd and an integer kâ¥2, the k-resultant modulus set, denoted by Îk(E), is defined asÎk(E)={âx1±x2±â¯Â±xkââFq:xjâE,j=1,2,â¦,k}, where âαâ=α12+â¯+αd2 for α=(α1,â¦,αd)âFqd. In this setting, the k-resultant modulus set problem is to determine the minimal cardinality of EâFqd such that Îk(E)=Fq or Fqâ. This problem is an extension of the ErdÅs-Falconer distance problem. In particular, we investigate the k-resultant modulus set problem with the restriction that the set EâFqd is contained in a specific algebraic variety. Energy estimates play a crucial role in our proof.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Finite Fields and Their Applications - Volume 48, November 2017, Pages 68-86
Journal: Finite Fields and Their Applications - Volume 48, November 2017, Pages 68-86
نویسندگان
David Covert, Doowon Koh, Youngjin Pi,