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Restriction theory of the Selberg sieve, with applications

Abstract:

The Selberg sieve provides majorants for certain arithmetic sequences, such as the primes and the twin primes. We prove an L^2-L^p restriction theorem for majorants of this type. An immediate application is to the estimation of exponential sums over prime k-tuples. Let a_1,...,a_k and b_1,...,b_k be positive integers. For t on the unit circle write h(t) := \sum_{n \in X} e(nt)$, where X is the set of all n <= N such that the numbers a_1n + b_1,..., a_kn + b_k are all prime. We obtain upp...

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Publication date:
2004-05-30
URN:
uuid:26631d0d-9544-436c-ab46-4328bf83f4f4
Source identifiers:
398500
Local pid:
pubs:398500
Keywords:

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