Oscillations of a given size of some arithmetic error terms
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- by Jerzy Kaczorowski and Kazimierz Wiertelak PDF
- Trans. Amer. Math. Soc. 361 (2009), 5023-5039 Request permission
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.References
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Additional Information
- Jerzy Kaczorowski
- Affiliation: Faculty of Mathematics and Computer Science, Adam Mickiewicz University, 61-614 Poznań, Poland.
- MR Author ID: 96610
- 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
- 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.
- © Copyright 2009 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 361 (2009), 5023-5039
- MSC (2000): Primary 11N05, 11N13, 11N25; Secondary 11M26
- DOI: https://doi.org/10.1090/S0002-9947-09-04803-X
- MathSciNet review: 2506435