Explicit estimates for and
Author:
Kevin S. McCurley
Journal:
Math. Comp. 42 (1984), 287296
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 Lfunctions, we prove explicit numerical bounds for of the form , .
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 R. Brent, "On the zeros of the Riemann zeta function in the critical strip," Math. Comp., v. 33, 1979, pp. 13611372. MR 537983 (80g:10033)
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 D. Davies, "An approximate functional equation for Dirichlet Lfunctions," Proc. Roy. Soc. London, v. 284, 1965, pp. 224236. MR 0173352 (30:3565)
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 K. S. McCurley, "Explicit zerofree regions for Dirichlet Lfunctions." (To appear.) MR 751161 (85k:11041)
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 K. S. McCurley, "Explicit estimates for the error term in the prime number theorem for arithmetic progressions," Math. Comp., v. 42, 1984, pp. 265285. MR 726004 (85e:11065)
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 J. B. Rosser & L. Schoenfeld, "Sharper bounds for the Chebyshev functions and ," Math. Comp., v. 29, 1975, pp. 243269. MR 0457373 (56:15581a)
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 Royal Society of London, Mathematical Tables Committee, Royal Society Depository of Unpublished Mathematical Tables, Table 83.
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 R. Spira, "Calculation of Dirichlet Lfunctions," Math. Comp., v. 23, 1969, pp. 489497. Microfiche supplement. MR 0247742 (40:1004a)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718198407260058
PII:
S 00255718(1984)07260058
Article copyright:
© Copyright 1984
American Mathematical Society
