Functiones et Approximatio Commentarii Mathematici

The class of the exceptional sets for a general asymptotic formula

Danilo Bazzanella and Riccardo Camerlo

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Abstract

We study the problem of the existence of a true exceptional set for an asymptotic formula, that is a minimal set --- up to finite modifications --- such that the asymptotic formula holds outside such a set. We give an analytic and a descriptive set theoretic characterisations for the existence of a true exceptional set, which we then apply by showing the non-existence of a true exceptional set in some well known situations. We prove in fact that, both from a category and a measure theoretic points of view, most asymptotic formulas do not have a true exceptional set.

Article information

Source
Funct. Approx. Comment. Math., Volume 51, Number 2 (2014), 347-362.

Dates
First available in Project Euclid: 26 November 2014

Permanent link to this document
https://projecteuclid.org/euclid.facm/1417010858

Digital Object Identifier
doi:10.7169/facm/2014.51.2.7

Mathematical Reviews number (MathSciNet)
MR3282632

Zentralblatt MATH identifier
1326.03057

Subjects
Primary: 03E15: Descriptive set theory [See also 28A05, 54H05] 11N37: Asymptotic results on arithmetic functions
Secondary: 11N05: Distribution of primes

Keywords
exceptional set asymptotic formula Borel set

Citation

Bazzanella, Danilo; Camerlo, Riccardo. The class of the exceptional sets for a general asymptotic formula. Funct. Approx. Comment. Math. 51 (2014), no. 2, 347--362. doi:10.7169/facm/2014.51.2.7. https://projecteuclid.org/euclid.facm/1417010858


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