The Large Sieve for 2 modulo Primes
نویسنده
چکیده
Let λ be a fixed integer, λ ≥ 2. Let s n be any strictly increasing sequence of positive integers satisfying s n ≤ n 15/14+o(1). In this paper we give a version of the large sieve inequality for the sequence λ sn. In particular, we prove that for π(X)(1 + o(1)) primes p, p ≤ X, the numbers λ sn , n ≤ X(log X) 2+ε are uniformly distributed modulo p.
منابع مشابه
On variants of the larger sieve
The large sieve has its origins in the work of Linnik and Rényi. It was developed to deal with sequences that avoid a positive proportion of residue classes. It was later simplified by Roth, Bombieri, Davenport, Halberstam, Montgomery, Gallagher and many others. For a survey see Montgomery [12] and Bombieri [1]. It is known that Montgomery’s large sieve [12] is a useful method when sifting sequ...
متن کامل15/14+o(1))] modulo primes
Let λ be a fixed integer, λ ≥ 2. Let s n be any strictly increasing sequence of positive integers satisfying s n ≤ n 15/14+o(1). In this paper we give a version of the large sieve inequality for the sequence λ sn. In particular, we prove that for π(X)(1 + o(1)) primes p, p ≤ X, the numbers λ sn , n ≤ X(log X) 2+ε are uniformly distributed modulo p.
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تاریخ انتشار 2005