Small gaps in coefficients of L-functions and B-free numbers in small intervals

2005/06/30 by Emmanuel Kowalski, Olivier Robert, Kowalski, Emmanuel +3
Mathematics · #11F12 #11F30 #11F66 #11L15 #11N25 #Advanced Mathematical Identities #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11F12 #msc:11F30 #msc:11F66 #msc:11L15 #msc:11N25

paper · pdf · doi:10.48550/arxiv.math/0507001

37 pages

arxiv created 2005/06/30 · openalex publication_date 2005/06/30 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We discuss questions related to the non-existence of gaps in the series defining modular forms and other arithmetic functions of various types, and improve results of Serre, Balog and Ono, and Alkan, using new results about exponential sums and the distribution of B-free numbers.

Citations

• Linear Equations in Variables which Lie in a Multiplicative Group
• Primes in arithmetic progressions to large moduli

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• Multiplicative functions in short intervals II
• On Bourgain's bound for short exponential sums and squarefree numbers
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• New small gaps between squarefree numbers