Algebra & Number Theory
- Algebra Number Theory
- Volume 9, Number 10 (2015), 2325-2346.
Polynomial values modulo primes on average and sharpness of the larger sieve
This paper is motivated by the following question in sieve theory. Given a subset and . Suppose that for every prime . How large can be? On the one hand, we have the bound from Gallagher’s larger sieve. On the other hand, we prove, assuming the truth of an inverse sieve conjecture, that the bound above can be improved (for example, to for small ). The result follows from studying the average size of as varies, when is the value set of a polynomial .
Algebra Number Theory, Volume 9, Number 10 (2015), 2325-2346.
Received: 17 December 2014
Revised: 19 July 2015
Accepted: 17 August 2015
First available in Project Euclid: 16 November 2017
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Shao, Xuancheng. Polynomial values modulo primes on average and sharpness of the larger sieve. Algebra Number Theory 9 (2015), no. 10, 2325--2346. doi:10.2140/ant.2015.9.2325. https://projecteuclid.org/euclid.ant/1510842448