Affiliation:
1. Department of Mathematics , University of Toronto , Canada ; Korea Institute for Advanced Study , Seoul , Korea
Abstract
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.
Reference7 articles.
1. [1] CHO, P. J.—KIM, H. H.: Logarithmic derivatives of Artin L-functions, Compos. Math. 149 (2013), no. 4, 568–586.
2. [2] CHO, P. J.—KIM, H. H.: Extreme residues of Dedekind zeta functions, Math. Proc. Cambridge. Philos. Soc. 163 (2017), no. 2, 369–380.
3. [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
4. [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
5. [5] IWANIEC, H.—KOWALSKI, E.: Analytic Number Theory. In: Amer. Math. Soc. Colloq. Publ. Vol. 53, American Mathematical Society, Providence, RI, 2004.
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献