کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
8895653 | 1630352 | 2018 | 37 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Trace of products in finite fields
ترجمه فارسی عنوان
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
چکیده انگلیسی
Let p be a prime number and let q=pr. If C and D are large subsets of Fqâ we study the trace of products cd with câC and dâD and show that it is well distributed in Fp. We give an optimal condition (up to an absolute constant factor) on the size of the subsets C and D to ensure that the trace of products cd takes any given value in Fp. We also give a condition (optimal up to an absolute constant factor in most cases) on the size of the subsets C and D to ensure that the trace of cd meets the set of k-th powers for kâ¥1, respectively the set of generators. Our method will enable us to take sets C and D whose size is substantially below q. Character sums and Gaussian sums over Fp and Fq will play an important role in the proofs. Some estimates lead to interesting combinatorial questions in finite fields.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Finite Fields and Their Applications - Volume 51, May 2018, Pages 93-129
Journal: Finite Fields and Their Applications - Volume 51, May 2018, Pages 93-129
نویسندگان
Cathy Swaenepoel,