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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Diophantine approximation with arithmetic functions, I


Authors: Emre Alkan, Kevin Ford and Alexandru Zaharescu
Journal: Trans. Amer. Math. Soc. 361 (2009), 2263-2275
MSC (2000): Primary 11N64, 11N36, 11K60
Published electronically: December 10, 2008
MathSciNet review: 2471917
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Abstract: We prove a strong simultaneous Diophantine approximation theorem for values of additive and multiplicative functions provided that the functions have certain regularity on the primes.


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Additional Information

Emre Alkan
Affiliation: Department of Mathematics, Koc University, Rumelifeneri Yolu, 34450, Sariyer, Istanbul, Turkey
Email: ealkan@ku.edu.tr

Kevin Ford
Affiliation: Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 W. Green Street, Urbana, Illinois 61801
Email: ford@math.uiuc.edu

Alexandru Zaharescu
Affiliation: Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 W. Green Street, Urbana, Illinois 61801
Email: zaharesc@math.uiuc.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-08-04822-8
PII: S 0002-9947(08)04822-8
Keywords: Diophantine approximation, additive functions, multiplicative functions
Received by editor(s): June 6, 2006
Published electronically: December 10, 2008
Additional Notes: The second author was supported in part by the National Science Foundation Grant DMS-0555367.
The third author was supported in part by the National Science Foundation Grant DMS-0456615.
Article copyright: © Copyright 2008 American Mathematical Society