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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Oscillations of a given size of some arithmetic error terms


Authors: Jerzy Kaczorowski and Kazimierz Wiertelak
Journal: Trans. Amer. Math. Soc. 361 (2009), 5023-5039
MSC (2000): Primary 11N05, 11N13, 11N25; Secondary 11M26
Published electronically: April 20, 2009
MathSciNet review: 2506435
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Abstract | References | Similar Articles | Additional Information

Abstract: A general method of estimating the number of oscillations of a given size of arithmetic error terms is developed. Special attention is paid to the remainder terms in the prime number formula, in the Dirichlet prime number theorem for primes in arithmetic progressions and to the remainder term in the asymptotic formula for the number of square free divisors of an integer.


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Additional Information

Jerzy Kaczorowski
Affiliation: Faculty of Mathematics and Computer Science, Adam Mickiewicz University, 61-614 Poznań, Poland.
Email: kjerzy@amu.edu.pl

Kazimierz Wiertelak
Affiliation: Faculty of Mathematics and Computer Science, Adam Mickiewicz University, 61-614 Poznań, Poland.
Email: wiertela@amu.edu.pl

DOI: https://doi.org/10.1090/S0002-9947-09-04803-X
Received by editor(s): July 18, 2007
Received by editor(s) in revised form: January 14, 2008
Published electronically: April 20, 2009
Additional Notes: Both authors were supported in part by KBN Grant N N201 1482 33.
Article copyright: © Copyright 2009 American Mathematical Society