Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-11T04:37:14.148Z Has data issue: false hasContentIssue false
  • English
  • Français

Rational Analogues of the Logarithm Function

Published online by Cambridge University Press:  03 November 2016

J. Lambek  and
L. Moser
Get access Rights & Permissions [Opens in a new window]

Extract

In this paper, we consider a sequence lr(x) (r = 1, 2, ..) of rational functions of a positive rational variable x, which approach log x as r→∞. Some properties of these functions are analogous to properties of the natural logarithm, and go over into the latter, when the limit r→∞ is taken. Except for pointing out such limiting results, we shall avoid transcendental methods.

Type
Research Article
Information
The Mathematical Gazette , Volume 40 , Issue 331 , February 1956 , pp. 5 - 7
Copyright
Copyright © Mathematical Association 1956

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Broderick, T. S., “On obtaining an estimate of the frequency of primes by means of elementary properties of integers”, J. London Math. Soc, 14 (1939) 303–310.10.1112/jlms/s1-14.4.303Google Scholar
2. Broderick, T. S., “On proving certain properties of primes by means of the methods of pure number theory”, Proc. Roy. Irish Soc, A 16 (1940), 17–24.Google Scholar
3. Behrend, F. A., “On obtaining an estimate of the frequency of primes by means of elementary properties of integers”, J. London Math. Soc, 15 (1940) 257–259.10.1112/jlms/s1-15.4.257Google Scholar
4. Behrend, F. A., “On the frequency of primes”, J. Proc. Roy. Soc, New South Wales, 25 (1942), 169–174.Google Scholar
5. Hardy, G. H. and Wright, E. M., An Introduction to the theory of numbers, (Oxford 1938).Google Scholar
6. Zassenhaus, H., “Uber die Existenz von Primzahlen in arithmetischen Progressionen”, Comment. Math. Helv. 22 (1949) 232–259.10.1007/BF02568058Google Scholar
7 Fogels, E. K., “On an elementary proof of the prime number theorem”, Latvyas P.S.R. Zinatnu Fiz. Math. Inst. Rakst. 2 (1950) 14–45.Google Scholar
8. Lambek, J. and Moser, L., “Elementary methods in the theory of distribution of primes”, abstract 577, Bull. Amer. Math. Soc, vol. 59 (1953) p. 527. Research Institute, Canadian Math. Congress.Google Scholar