On the L¹ norm of an exponential sum involving the divisor function

2017/04/19 by D. A. Goldston, Goldston, D. A., Mayank Pandey +1 · 1 citation
Mathematics · #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1704.05953

openalex publication_date 2017/04/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we obtain bounds on the L¹ norm of the sum ∑_{n≤ x}τ(n) e(αn) where τ(n) is the divisor function.

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• Exponential sums over primes are unbounded

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