1. bookVolume 16 (2021): Issue 1 (June 2021)
Journal Details
License
Format
Journal
First Published
30 Dec 2013
Publication timeframe
1 time per year
Languages
English
access type Open Access

Extreme Values of Euler-Kronecker Constants

Published Online: 30 Oct 2021
Page range: 41 - 52
Received: 13 Jan 2021
Accepted: 06 Apr 2021
Journal Details
License
Format
Journal
First Published
30 Dec 2013
Publication timeframe
1 time per year
Languages
English
Abstract

In a family of Sn-fields (n ≤ 5), we show that except for a density zero set, the lower and upper bounds of the Euler-Kronecker constants are (n − 1) log log dK+ O(log log log dK) and loglog dK + O(log log log dK), resp., where dK is the absolute value of the discriminant of a number field K.

Keywords

MSC 2010

[1] CHO, P. J.—KIM, H. H.: Logarithmic derivatives of Artin L-functions, Compos. Math. 149 (2013), no. 4, 568–586. Search in Google Scholar

[2] CHO, P. J.—KIM, H. H.: Extreme residues of Dedekind zeta functions, Math. Proc. Cambridge. Philos. Soc. 163 (2017), no. 2, 369–380. Search in Google Scholar

[3] CHO, P. J.—KIM, H. H.: Moments of logarithmic derivatives of L-functions, J. Number Theory 183 (2018), 40–61.10.1016/j.jnt.2017.08.017 Search in Google Scholar

[4] IHARA, Y.: On the Euler-Kronecker constants of global fields and primes with small norms, In: Algebraic Geometry and Number Theory, Progress in Mathematics, Vol. 253, Birkhäuser, Boston, MA, 2006, pp. 407–451.10.1007/978-0-8176-4532-8_5 Search in Google Scholar

[5] IWANIEC, H.—KOWALSKI, E.: Analytic Number Theory. In: Amer. Math. Soc. Colloq. Publ. Vol. 53, American Mathematical Society, Providence, RI, 2004. Search in Google Scholar

[6] KLINGEN, N.: Arithmetical Similarities. In: Prime decomposition and finite group theory. In: Oxford Mathematical Monographs. Oxford Science Publications. The Clarendon Press, Oxford University Press, New York, 1998. Search in Google Scholar

[7] KOWALSKI, E.—MICHEL, P.: Zeros of families of automorphic L-functions close to 1, Pacific. J. Math. 207 (2002), no. 2, 411–431. Search in Google Scholar

Recommended articles from Trend MD

Plan your remote conference with Sciendo