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Oscillations of a given size of some arithmetic error terms
Author(s):
Jerzy
Kaczorowski;
Kazimierz
Wiertelak
Journal:
Trans. Amer. Math. Soc.
361
(2009),
5023-5039.
MSC (2000):
Primary 11N05, 11N13, 11N25;
Secondary 11M26
Posted:
April 20, 2009
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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 Poznan, Poland.
Email:
kjerzy@amu.edu.pl
Kazimierz
Wiertelak
Affiliation:
Faculty of Mathematics and Computer Science, Adam Mickiewicz University, 61-614 Poznan, Poland.
Email:
wiertela@amu.edu.pl
DOI:
10.1090/S0002-9947-09-04803-X
PII:
S 0002-9947(09)04803-X
Received by editor(s):
July 18, 2007
Received by editor(s) in revised form:
January 14, 2008
Posted:
April 20, 2009
Additional Notes:
Both authors were supported in part by KBN Grant N N201 1482 33.
Copyright of article:
Copyright
2009,
American Mathematical Society
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