منابع مشابه
The Sum-product Estimate for Large Subsets of Prime Fields
Let Fp be the field of prime order p. It is known that for any integer N ∈ [1, p] one can construct a subset A ⊂ Fp with |A| = N such that max{|A+ A|, |AA|} p|A|. One of the results of the present paper implies that if A ⊂ Fp with |A| > p2/3, then max{|A+ A|, |AA|} p|A|.
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Let F p be the field of a prime order p. It is known that for any integer N ∈ [1, p] one can construct a subset A ⊂ F p with |A| = N such that max{|A + A|, |AA|} ≪ p 1/2 |A| 1/2. In the present paper we prove that if A ⊂ F p with |A| > p 2/3 , then max{|A + A|, |AA|} ≫ p 1/2 |A| 1/2 .
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A set A of primes p involving numbers such as abt + c, where |a|, |b|, |c| = O(1) and t → ∞, is defined. An algorithm for computing discrete logs in the finite field of order p with p ∈ A is suggested. Its heuristic expected running time is Lp[ 1 3 ; ( 32 9 )1/3] for ( 32 9 )1/3 = 1.526 · · · , where Lp[α;β] = exp((β + o(1)) ln α p(ln ln p)1−α) as p → ∞, 0 < α < 1, and 0 < β. At present, the mo...
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ROBERT C. RHOADES Abstra t. We show that the prime divisors of a random polynomial in Fq[t] are typi ally Poisson Distributed . This result is analogous to the result in Z of Granville [1℄. Along the way, we use a sieve developed by Granville and Soundararajan [2℄ to give a simple proof of the Erdös-Ka theorem in the fun tion eld setting. This approa h gives stronger results about the moments o...
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ژورنال
عنوان ژورنال: Bulletin of the Australian Mathematical Society
سال: 2019
ISSN: 0004-9727,1755-1633
DOI: 10.1017/s0004972719000303