Hostname: page-component-8448b6f56d-qsmjn Total loading time: 0 Render date: 2024-04-18T16:13:37.377Z Has data issue: false hasContentIssue false
  • English
  • Français

Generalised Euler constants

Published online by Cambridge University Press:  20 January 2009

J. Knopfmacher
J. Knopfmacher
Affiliation:
University of Witwatersrand, Johannesburg, South Africa
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let the Laurent expansion of the Riemann zeta function ξ(s) about s=1 be written in the form

It has been discovered independently by many authors that, in terms of this notation, the coefficient

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 21 , Issue 1 , March 1978 , pp. 25 - 32
Copyright
Copyright © Edinburgh Mathematical Society 1978

References

REFERENCES

(1) Bateman, P. T. and Diamond, H. G., Asymptotic distribution of Beurling's general- ized prime numbers, Studies in Number Theory, MAA Studies in Math., Vol. 6 (Prentice-Hall, 1969).Google Scholar
(2) Berndt, B. C., On the Hurwitz zeta function. Rocky Mountain J. Math. 2 (1972), 151–157.CrossRefGoogle Scholar
(3) Berndt, B. C., Character analogues of the Poisson and Euler-MacLaurin summation formulas with applications, J. Number Theory 7 (1975), 413–445.CrossRefGoogle Scholar
(4) Briggs, W. E., The irrationality of y or of sets of similar constants, K. Norske Vid. Selsk. Forh. (Trondheim) 34 (1961), 25–28.Google Scholar
(5) Briggs, W. E.,& Buschman, R. G., The power series coefficients of functions defined by Dirichlet series, Illinois J. Math. 5 (1961), 43–44.CrossRefGoogle Scholar
(6) Briggs, W. E. & Chowla, S., The power series coefficients of ζ(s), Amer. Math. Monthly 62 (1955), 323–325.Google Scholar
(7) Cohen, E., On the average number of direct factors of a finite abelian group. Acta Arith. 6 (1960), 159–173.CrossRefGoogle Scholar
(8) Knopfmacher, J., Arithmetical properties of finite rings and algebras, and analytic number theory, I-V, J. Reine Angew. Math. 252 (1972), 16–43, 254 (1972), 74–99, 259 (1973), 157–170, 270 (1974), 97–114, 271 (1974), 95–121.Google Scholar
(9) Knopfmacher, J., Abstract Analytic Number Theory (North-Holland Publ. Co., 1975).Google Scholar
(10) Landau, E., Über die zueinem algebraischen Zahlkörper gehörige Zetafunktion …, J. Reine Angew. Math. 125 (1903), 64–188.Google Scholar
(11) Landau, E., Über eine idealtheoretische Funktion. Trans. Amer. Math. Soc. 13 (1912), 1–21.Google Scholar
(12) Landau, E., Einführung in die elementare und analytische Theorie der algebraischen Zahlen und der Ideale (Chelsea Publ. Co., 1949 reprint).Google Scholar
(13) Lehmer, D. H., Euler constants for arithmetical progressions, Acta Arith. 27 (1975), 125–142.CrossRefGoogle Scholar
(14) Siegel, C. L., Lectures on Advanced Analytic Number Theory (Tata Inst, of Fund. Research, 1961).Google Scholar
(15) Van Veen, S. C., Math. Reviews 29 (1965) #2232.Google Scholar
(16) Widder, D. V., The Laplace Transform (Princeton Univ. Press, 1941).Google Scholar