Hostname: page-component-5db58dd55d-d6ndz Total loading time: 0 Render date: 2026-06-23T02:51:58.685Z Has data issue: false hasContentIssue false
  • English
  • Français

TRANSCENDENCE OF GENERALISED EULER–KRONECKER CONSTANTS

Part of: Diophantine approximation, transcendental number theory

Published online by Cambridge University Press:  10 July 2023

NEELAM KANDHIL Open the ORCID record for NEELAM KANDHIL [Opens in a new window]  and
RASHI LUNIA Open the ORCID record for RASHI LUNIA [Opens in a new window]
NEELAM KANDHIL
Affiliation:
Max-Planck-Institut für Mathematik, Vivatsgasse 7, D-53111 Bonn, Germany e-mail: kandhil@mpim-bonn.mpg.de
RASHI LUNIA*
Affiliation:
The Institute of Mathematical Sciences, A CI of Homi Bhabha National Institute, CIT Campus, Taramani, Chennai 600 113, India
*
e-mail: rashisl@imsc.res.in
Get access Rights & Permissions [Opens in a new window]

Abstract

We introduce some generalisations of the Euler–Kronecker constant of a number field and study their arithmetic nature.

Keywords

linear forms in logarithmsgeneralised Euler–Kronecker constants

MSC classification

Primary: 11J86: Linear forms in logarithms; Baker's method
Secondary: 11J81: Transcendence (general theory)

Information

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 109 , Issue 3 , June 2024 , pp. 464 - 470
Check for updates
Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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.)

Article purchase

Temporarily unavailable

Footnotes

The second author would like to thank Number Theory plan project, Department of Atomic Energy, for financial support.

References

Diamond, H. and Ford, K., ‘Generalized Euler constants’, Math. Proc. Cambridge Philos. Soc. 145(1) (2008), 27–41.CrossRefGoogle Scholar
Euler, L., ‘De Progressionibus harmonicis observationes’, Comment. Acad. Sci. Petropolitanae 7 (1740), 150–161.Google Scholar
Ihara, Y., ‘The Euler–Kronecker invariants in various families of global fields’, in: Arithmetic, Geometry and Coding Theory (AGCT 2005) (eds. F. Rodier and S. Vladut), Séminaire et Congrès, 21 (Société Mathématique de France, Paris, 2006), 79–102.Google Scholar
Lagarias, J. C., ‘Euler’s constant: Euler’s work and modern developments’, Bull. Amer. Math. Soc. 50 (2013), 527–628.CrossRefGoogle Scholar
Lindemann, F., ‘Über die Zahl $\pi$ ’, Math. Ann. 20(2) (1882), 213–225.CrossRefGoogle Scholar
Murty, M. R., Problems in Analytic Number Theory, 2nd edn (Springer, New York, 2008).Google Scholar
Murty, M. R. and Esmonde, J., Problems in Algebraic Number Theory (Springer, New York, 2005).Google Scholar
Murty, M. R. and Zaytseva, A., ‘Transcendence of generalized Euler constants’, Amer. Math. Monthly 120(1) (2013), 48–54.CrossRefGoogle Scholar
Rosen, M., ‘A generalization of Mertens’ theorem’, J. Ramanujan Math. Soc. 14(1) (1999), 1–19.Google Scholar