Das asymptotische Verhalten von Summen über multiplikative Funktionen. II

Wirsing, Eduard

doi:10.1007/bf02280301

Cited by 160 publications

(120 citation statements)

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“…Let A be the set of integers not divisible by any prime in P and let a(n) = 1 if n ∈ A and a(n) = 0 otherwise. Wirsing proved (see page 417 of [18]) that…”

Section: Corollary 61 Follows Immediately From (63 Ab)mentioning

confidence: 99%

An uncertainty principle for arithmetic sequences

Granville

Soundararajan

2007

Ann. Math.

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Analytic number theorists usually seek to show that sequences which appear naturally in arithmetic are "well-distributed" in some appropriate sense. In various discrepancy problems, combinatorics researchers have analyzed limitations to equidistribution, as have Fourier analysts when working with the "uncertainty principle". In this article we find that these ideas have a natural setting in the analysis of distributions of sequences in analytic number theory, formulating a general principle, and giving several examples.

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“…Let A be the set of integers not divisible by any prime in P and let a(n) = 1 if n ∈ A and a(n) = 0 otherwise. Wirsing proved (see page 417 of [18]) that…”

Section: Corollary 61 Follows Immediately From (63 Ab)mentioning

confidence: 99%

An uncertainty principle for arithmetic sequences

Granville

Soundararajan

2007

Ann. Math.

View full text Add to dashboard Cite

show abstract

“…The intricate proof of Wirsing formula appears in [36]. It is also assembled in various papers, such as [12], [27, p. 195], and discussed in [23, p. 70], [33, p. 308].…”

Section: Wirsing Formulamentioning

confidence: 99%