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Author(s)

Harman G

Publication year1997

Publication title

proceedings of the london mathematical society

Resource typeJournals

PublisherOxford University Press

Let a n be an increasing sequence of positive reals with a n → ∞ as n → ∞. Necessary and sufficient conditions are obtained for each of the sequences [ α a n ] , [ α a n] , [a nα ] to take on infinitely many prime values for almost all α > rβ. For example, the sequence α a n is infinitely often prime for almost all α > 0 if and only if there is a subsequence of the a n , say b n , with b n + 1 > b n + 1 and with the series ∑ 1 /b ndivergent. Asymptotic formulae are obtained when the sequences considered are lacunary. An earlier result of the author reduces the problem to estimating the measure of overlaps of certain sets, and sieve methods are used to obtain the correct order upper bounds. 1991 Mathematics Subject Classification : primary 11N05; secondary 11K99, 11N36.

Subject(s)biology , bounded function , combinatorics , computer science , discrete mathematics , economics , finance , genetics , integer (computer science) , lacunary function , mathematical analysis , mathematics , order (exchange) , paleontology , prime (order theory) , prime number , programming language , sequence (biology) , series (stratigraphy) , subsequence

Language(s)English

SCImago Journal Rank1.899

H-Index65

eISSN1460-244X

pISSN0024-6115

DOI10.1112/s0024611597000415

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