Local variation of euler products

Hugh L. Montgomery; Robert C. Vaughan

doi:10.7169/facm/1229696576

Local variation of euler products

Hugh L. Montgomery, Robert C. Vaughan

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We determine how big an Euler product can be at s₂, when its size at s₁ is known, and apply this via Halász's method to bound the mean value of a multiplicative function in terms of the size of the generating Dirichlet series.

Original language	English (US)
Pages (from-to)	273-288
Number of pages	16
Journal	Functiones et Approximatio, Commentarii Mathematici
Volume	39
Issue number	2
DOIs	https://doi.org/10.7169/facm/1229696576
State	Published - 2008

All Science Journal Classification (ASJC) codes

General Mathematics

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10.7169/facm/1229696576

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title = "Local variation of euler products",

abstract = "We determine how big an Euler product can be at s2, when its size at s1 is known, and apply this via Hal{\'a}sz's method to bound the mean value of a multiplicative function in terms of the size of the generating Dirichlet series.",

author = "Montgomery, {Hugh L.} and Vaughan, {Robert C.}",

note = "Funding Information: Research supported in part by NSF Grant DMS-0653529. Research supported in part by NSA Grant H98230-06-1-0077. Publisher Copyright: {\textcopyright} Wydawnictwo Naukowe UAM, Pozna{\'n} 2008.",

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Local variation of euler products

Abstract

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