Explicit estimates for the error term in the prime number theorem for arithmetic progressions
Author:
Kevin S. McCurley
Journal:
Math. Comp. 42 (1984), 265-285
MSC:
Primary 11N13; Secondary 11-04, 11Y35
DOI:
https://doi.org/10.1090/S0025-5718-1984-0726004-6
MathSciNet review:
726004
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Abstract | References | Similar Articles | Additional Information
Abstract: We give explicit numerical estimates for the Chebyshev functions and
for certain nonexceptional moduli k. For values of
and b, a constant c is tabulated such that
, provided
,
, and
. The methods are similar to those used by Rosser and Schoenfeld in the case
, but are based on explicit estimates of
and an explicit zero-free region for Dirichlet L-functions.
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Additional Information
DOI:
https://doi.org/10.1090/S0025-5718-1984-0726004-6
Article copyright:
© Copyright 1984
American Mathematical Society