Linnik's large sieve and the L¹ norm of exponential sums

2019/08/19 by Eckels, Emily, Jin, Steven, Ledoan, Andrew +1
#11L03 #11L07 #11L20 #11N36 #42A05 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1908.06946

Abstract

The method of proof of Balog and Ruzsa and the large sieve of Linnik are used to investigate the behaviour of the L¹ norm of a wide class of exponential sums over the square-free integers and the primes. Further, a new proof of the lower bound due to Vaughan for the L¹ norm of an exponential sum with the von Mangoldt Λ function over the primes is furnished. Ramanujan's sum arises naturally in the proof, which also employs Linnik's large sieve.

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