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arXiv · 1908.06946

Linnik's large sieve and the $L^{1}$ norm of exponential sums

Emily Eckels·Steven Jin·Andrew Ledoan·Brian Tobin
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Abstract

The method of proof of Balog and Ruzsa and the large sieve of Linnik are used to investigate the behaviour of the $L^{1}$ 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 $L^{1}$ 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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Emily Eckels, Steven Jin, Andrew Ledoan, Brian Tobin. 2019-08-19. Linnik's large sieve and the $L^{1}$ norm of exponential sums. https://arxiv.org/abs/1908.06946

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