Transcendence of Generalized Euler Constants

2012/12/02 by M. Ram Murty, Anastasia Zaytseva · 2 citations
Mathematics · #Analytic Number Theory Research #Advanced Mathematical Identities #Advanced Algebra and Geometry

paper · doi:10.4169/amer.math.monthly.120.01.048

openalex publication_date 2012/12/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/06/26

Abstract

We consider a class of analogues of Euler's ᵞ constant and use Baker's theory of linear forms in logarithms to study its arithmetic properties. In particular, we show that with at most one exception, all of these analogues are transcendental.

Citations

• Euler–Lehmer constants and a conjecture of Erdös

Cited by

• Euler's constant [wikipedia]
• Transcendental number [wikipedia]

Related

• On the Algebraic Independence of a Set of Generalized Constants
• Euler’s constant: Euler’s work and modern developments
• A hypergeometric approach, via linear forms involving logarithms, to criteria for irrationality of Euler’s constant
• Transcendence Results for Γ⁽ⁿ⁾(1) and Related Sequences of Generalized Constants
• A note on the generalized Euler numbers and polynomials