Explicit estimates for and

Author:
Kevin S. McCurley

Journal:
Math. Comp. **42** (1984), 287-296

MSC:
Primary 11N56

MathSciNet review:
726005

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Abstract: Let be the sum of the logarithms of the primes not exceeding *x* that are congruent to *l* modulo 3, where *l* is 1 or 2. By the prime number theorem for arithmetic progressions, as . Using information concerning zeros of Dirichlet *L*-functions, we prove explicit numerical bounds for of the form , .

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DOI:
http://dx.doi.org/10.1090/S0025-5718-1984-0726005-8

Article copyright:
© Copyright 1984
American Mathematical Society