Estimates for the Chebyshev function $\psi (x)-\theta (x)$
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- by N. Costa Pereira PDF
- Math. Comp. 44 (1985), 211-221 Request permission
Corrigendum: Math. Comp. 48 (1987), 447.
Abstract:
A simple approximation for the difference $\psi (x) - \theta (x)$ is established by elementary methods. This approximation is used to obtain several estimates for $\psi (x) - \theta (x)$ which are sharper than those previously given in the literature.References
- K. I. Appel & J. B. Rosser, Table for Estimating Functions of Primes, Comm. Res. Div. Tech. Rep. No. 4, Institute for Defense Analysis, Princeton, N.J., 1961.
D. N. Lehmer, List of Prime Numbers from 1 to 10006721, Carnegie Inst. of Washington, Publ. No. 165, Washington, 1914.
- J. Barkley Rosser and Lowell Schoenfeld, Approximate formulas for some functions of prime numbers, Illinois J. Math. 6 (1962), 64–94. MR 137689
- J. Barkley Rosser and Lowell Schoenfeld, Sharper bounds for the Chebyshev functions $\theta (x)$ and $\psi (x)$, Math. Comp. 29 (1975), 243–269. MR 457373, DOI 10.1090/S0025-5718-1975-0457373-7
- J. Barkley Rosser and Lowell Schoenfeld, Sharper bounds for the Chebyshev functions $\theta (x)$ and $\psi (x)$, Math. Comp. 29 (1975), 243–269. MR 457373, DOI 10.1090/S0025-5718-1975-0457373-7
Additional Information
- © Copyright 1985 American Mathematical Society
- Journal: Math. Comp. 44 (1985), 211-221
- MSC: Primary 11A25; Secondary 11N45, 11Y35, 33A70
- DOI: https://doi.org/10.1090/S0025-5718-1985-0771046-9
- MathSciNet review: 771046