Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



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
MathSciNet review: 726004
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We give explicit numerical estimates for the Chebyshev functions $ \psi (x;k,l)$ and $ \theta (x;k,l)$ for certain nonexceptional moduli k. For values of $ \varepsilon $ and b, a constant c is tabulated such that $ \vert\psi (x;k,l) - x/\varphi (k)\vert < \varepsilon x/\varphi (k)$, provided $ (k,l) = 1$, $ x \geqslant \exp (c{\log ^2}k)$, and $ k \geqslant {10^b}$. The methods are similar to those used by Rosser and Schoenfeld in the case $ k = 1$, but are based on explicit estimates of $ N(T,\chi )$ and an explicit zero-free region for Dirichlet L-functions.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 11N13, 11-04, 11Y35

Retrieve articles in all journals with MSC: 11N13, 11-04, 11Y35

Additional Information

Article copyright: © Copyright 1984 American Mathematical Society