On the Exponential Large Sieve Inequality for Sparse Sequences modulo Primes
نویسندگان
چکیده
FOR SPARSE SEQUENCES MODULO PRIMES MEI-CHU CHANG, BRYCE KERR, AND IGOR E. SHPARLINSKI Abstract. We complement the argument of M. Z. Garaev (2009) with several other ideas to obtain a stronger version of the large sieve inequality with sparse exponential sequences of the form λn . In particular, we obtain a result which is non-trivial for monotonically increasing sequences S “ tsnun“1 provided sn ď n2`op1q, whereas the original argument of M. Z. Garaev requires sn ď n15{14`op1q in the same setting. We also give an application of our result to arithmetic properties of integers with almost all digits prescribed.
منابع مشابه
The Large Sieve for 2 modulo Primes
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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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