Estimates for the Chebyshev function

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 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. 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 and ,"*Math. Comp.*, v. 29, 1975, pp. 243-269. MR**0457373 (56:15581a)****[5]**L. Schoenfeld, "Sharper bounds for the Chebyshev functions and . 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