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