The Geometric M\"obius function and quadratic character sums Article Swipe

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Mark Shusterman ·

YOU? · · 2018 · Open Access ·

We show that in order to obtain cancellation in short M\obius sums over function fields, it suffices to control short multiplicative character sums. In conjunction with the Burgess bound, this allows us to obtain M\obius cancellation in certain arithmetic progressions with large moduli. Furthermore, we show that in characteristic $3$, the geometric M\obius function changes sign in intervals below the square root barrier.

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Character (mathematics) Mathematics Moduli Function (biology) Sign (mathematics) Multiplicative function Square root Quadratic equation Square (algebra) Pure mathematics Combinatorics Mathematical analysis Geometry Physics Quantum mechanics Evolutionary biology Biology

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Type: article
Language: en
Landing Page: https://arxiv.org/pdf/1808.04001
OA Status: green
Cited By: 7
References: 16
Related Works: 20
OpenAlex ID: https://openalex.org/W2887577512

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Title: The Geometric M\"obius function and quadratic character sums

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Type: article

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Language: en

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Publication year: 2018

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Publication date: 2018-08-12

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Authors: Mark Shusterman

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Landing page: https://arxiv.org/pdf/1808.04001

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Concepts: Character (mathematics), Mathematics, Moduli, Function (biology), Sign (mathematics), Multiplicative function, Square root, Quadratic equation, Square (algebra), Pure mathematics, Combinatorics, Mathematical analysis, Geometry, Physics, Quantum mechanics, Evolutionary biology, Biology

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Cited by: 7

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