Exponential sum estimates over prime fields
نویسندگان
چکیده
منابع مشابه
Slightly Improved Sum-product Estimates in Fields of Prime Order
Let Fp be the field of residue classes modulo a prime number p and let A be a nonempty subset of Fp. In this paper we show that if |A| p , then max{|A ± A|, |AA|} |A|; if |A| p, then max{|A ± A|, |AA|} v min{|A|( |A| p0.5 ), |A|( p |A| )}. These results slightly improve the estimates of Bourgain-Garaev and Shen. Sum-product estimates on different sets are also considered.
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Let F be a field with positive odd characteristic p. We prove a variety of new sum-product type estimates over F . They are derived from the theorem that the number of incidences between m points and n planes in the projective three-space PG(3, F ), with m ≥ n = O(p), is O(m √ n+ km), where k denotes the maximum number of collinear planes. The main result is a significant improvement of the sta...
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In this paper we extend the exponential sum results from [B-K] and [B-G-K] for prime moduli to composite moduli q involving a bounded number of prime factors. In particular, we obtain nontrivial bounds on the exponential sums associated to multiplicative subgroups H of size q, for any given δ > 0. The method consists in first establishing a ‘sum-product theorem’ for general subsets A of Z. If q...
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This article presents a systematic study for structure of finite wavelet frames over prime fields. Let $p$ be a positive prime integer and $mathbb{W}_p$ be the finite wavelet group over the prime field $mathbb{Z}_p$. We study theoretical frame aspects of finite wavelet systems generated by subgroups of the finite wavelet group $mathbb{W}_p$.
متن کاملInequivalent representations of matroids over prime fields
Article history: Received 30 March 2011 Accepted 18 February 2013 Available online 15 March 2013
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ژورنال
عنوان ژورنال: International Journal of Number Theory
سال: 2019
ISSN: 1793-0421,1793-7310
DOI: 10.1142/s1793042120500153