Amplification Arguments for Large Sieve Inequalities
نویسنده
چکیده
We give a new proof of the arithmetic large sieve inequality based on an amplification argument, and use a similar method to prove a new sieve inequality for classical holomorphic cusp forms. A sample application of the latter is also given. 1. The classical large sieve The classical arithmetic large sieve inequality states that, for any real numbers N , Q > 1, any choice of subsets Ωp ⊂ Z/pZ for primes p 6 Q, we have (1) |{n 6 N | n (mod p) / ∈ Ωp for p 6 Q}| 6 ∆ H where H = ∑[
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