Estimates for the Chebyshev function 𝜓(𝑥)-𝜃(𝑥)-Reference-Cited by-同舟云学术

Estimates for the Chebyshev function 𝜓(𝑥)-𝜃(𝑥)

Published:1985 Issue:169 Volume:44 Page:211-221
ISSN:0025-5718
Container-title:Mathematics of Computation
language:en
Short-container-title:Math. Comp.

Author:

Costa Pereira N.

Abstract

A simple approximation for the difference ψ ( x ) − θ ( x ) \psi (x) - \theta (x) is established by elementary methods. This approximation is used to obtain several estimates for ψ ( x ) − θ ( x ) \psi (x) - \theta (x) which are sharper than those previously given in the literature.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,Computational Mathematics,Algebra and Number Theory

Link

http://www.ams.org/mcom/1985-44-169/S0025-5718-1985-0771046-9/S0025-5718-1985-0771046-9.pdf

Reference5 articles.

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. Approximate formulas for some functions of prime numbers;Rosser, J. Barkley;Illinois J. Math.,1962

4. Sharper bounds for the Chebyshev functions 𝜃(𝑥) and 𝜓(𝑥);Rosser, J. Barkley;Math. Comp.,1975

5. Sharper bounds for the Chebyshev functions 𝜃(𝑥) and 𝜓(𝑥);Rosser, J. Barkley;Math. Comp.,1975

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