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Estimates for the Chebyshev function $ \psi(x)-\theta (x)$


Author: N. Costa Pereira
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
Corrigendum: Math. Comp. 48 (1987), 447.
MathSciNet review: 771046
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Abstract | References | Similar Articles | Additional Information

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

  • [1] 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.
  • [2] D. N. Lehmer, List of Prime Numbers from 1 to 10006721, Carnegie Inst. of Washington, Publ. No. 165, Washington, 1914.
  • [3] J. B. Rosser & L. Schoenfeld, "Approximate formulas for some functions of prime numbers," Illinois J. Math., v. 6, 1962, pp. 64-94. MR 0137689 (25:1139)
  • [4] J. B. Rosser & L. Schoenfeld, "Sharper bounds for the Chebyshev functions $ \psi (x)$ and $ \theta (x)$," Math. Comp., v. 29, 1975, pp. 243-269. MR 0457373 (56:15581a)
  • [5] L. Schoenfeld, "Sharper bounds for the Chebyshev functions $ \psi (x)$ and $ \theta (x)$. II," Math. Comp., v. 30, 1976, pp. 337-360. MR 0457374 (56:15581b)

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DOI: https://doi.org/10.1090/S0025-5718-1985-0771046-9
Article copyright: © Copyright 1985 American Mathematical Society

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