Estimates of for large values of

Author:
Pierre Dusart

Journal:
Math. Comp. **71** (2002), 1137-1168

MSC (2000):
Primary 11N13, 11N56; Secondary 11Y35, 11Y40

DOI:
https://doi.org/10.1090/S0025-5718-01-01351-5

Published electronically:
November 21, 2001

MathSciNet review:
1898748

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Abstract | References | Similar Articles | Additional Information

Abstract: We extend a result of Ramaré and Rumely, 1996, about the Chebyshev function in arithmetic progressions. We find a map such that and , whereas is a constant. Now we are able to show that, for ,

and, for ,

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Additional Information

**Pierre Dusart**

Affiliation:
Département de Math., LACO, 123 avenue Albert Thomas, 87060 Limoges cedex, France

Email:
dusart@unilim.fr

DOI:
https://doi.org/10.1090/S0025-5718-01-01351-5

Keywords:
Bounds for basic functions,
arithmetic progression

Received by editor(s):
February 23, 1998

Received by editor(s) in revised form:
December 17, 1998, and August 21, 2000

Published electronically:
November 21, 2001

Article copyright:
© Copyright 2001
American Mathematical Society