Estimates for the Chebyshev function

Author:
N. Costa Pereira

Journal:
Math. Comp. **44** (1985), 211-221

MSC:
Primary 11A25; Secondary 11N45, 11Y35, 33A70

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 is established by elementary methods. This approximation is used to obtain several estimates for which are sharper than those previously given in the literature.

**[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. Barkley Rosser and Lowell Schoenfeld,*Approximate formulas for some functions of prime numbers*, Illinois J. Math.**6**(1962), 64–94. MR**0137689****[4]**J. Barkley Rosser and Lowell Schoenfeld,*Sharper bounds for the Chebyshev functions 𝜃(𝑥) and 𝜓(𝑥)*, Math. Comp.**29**(1975), 243–269. Collection of articles dedicated to Derrick Henry Lehmer on the occasion of his seventieth birthday. MR**0457373**, 10.1090/S0025-5718-1975-0457373-7**[5]**Lowell Schoenfeld,*Sharper bounds for the Chebyshev functions 𝜃(𝑥) and 𝜓(𝑥). II*, Math. Comp.**30**(1976), no. 134, 337–360. MR**0457374**, 10.1090/S0025-5718-1976-0457374-X

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DOI:
https://doi.org/10.1090/S0025-5718-1985-0771046-9

Article copyright:
© Copyright 1985
American Mathematical Society