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Transcendence of generalized Euler-Kronecker constants

Neelam Kandhil, Rashi Lunia

Abstract

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

Transcendence of generalized Euler-Kronecker constants

Abstract

We introduce some generalizations of the Euler-Kronecker constant of a number field and study their arithmetic nature.
Paper Structure (4 sections, 8 theorems, 33 equations)

This paper contains 4 sections, 8 theorems, 33 equations.

Table of Contents

  1. Introduction and Preliminaries
  2. Preliminaries and Lemmas
  3. Generalized Euler-Kronecker constants
  4. Proof of Theorem \ref{['trans']}

Key Result

Theorem 1.1

(Murty and Zaytseva) At most one number in the infinite list $\{\gamma(\Omega)\}$, as $\Omega$ varies over all finite subsets of distinct primes, is algebraic.

Theorems & Definitions (12)

  • Theorem 1.1
  • Theorem 1.2
  • Lemma 2.1
  • Lemma 2.2
  • proof
  • Lemma 2.3: Lindemann FL
  • Lemma 3.1
  • proof
  • Lemma 3.2
  • proof
  • ...and 2 more