Discriminant and integral basis of number fields defined by exponential Taylor polynomials

Authors

Ankita Jindal, Indian Statistical Institute Bangalore
Sudesh K. Khanduja, Indian Institute of Science Education and Research Mohali

Article Type

Research Article

Publication Title

Proceedings of the Edinburgh Mathematical Society

Abstract

Let Kn = ℚ(αn) be a family of algebraic number fields where αn ϵ ℂ is a root of the nth exponential Taylor polynomial (equation presented) In this paper, we give a formula for the exact power of any prime p dividing the discriminant of Kn in terms of the p-adic expansion of n. An explicit p-integral basis of Kn is also given for each prime p. These p-integral bases quickly lead to the construction of an integral basis of Kn.

First Page

528

Last Page

541

DOI

10.1017/S0013091524000105

Publication Date

5-8-2024

Recommended Citation

Jindal, Ankita and Khanduja, Sudesh K., "Discriminant and integral basis of number fields defined by exponential Taylor polynomials" (2024). Journal Articles. 4716.
https://digitalcommons.isical.ac.in/journal-articles/4716