The R₂ measure for totally positive algebraic integers

• Autorzy: V. Flammang
• Języki publikacji: EN

Abstrakty

EN

Let α be a totally positive algebraic integer of degree d, i.e., all of its conjugates $α₁ = α,..., α_{d}$ are positive real numbers. We study the set 𝓡₂ of the quantities $(∏_{i=1}^{d} (1 + α²_{i})^{1/2})^{1/d}$. We first show that √2 is the smallest point of 𝓡₂. Then, we prove that there exists a number l such that 𝓡₂ is dense in (l,∞). Finally, using the method of auxiliary functions, we find the six smallest points of 𝓡₂ in (√2,l). The polynomials involved in the auxiliary function are found by a recursive algorithm.

Kategorie tematyczne

• 11R06: PV-numbers and generalizations; other special algebraic numbers; Mahler measure
• 11Y40: Algebraic number theory computations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2016
• Tom: 144
• Numer: 1
• Strony: 45-53

Daty

wydano

2016

Twórcy

autor

V. Flammang

• UMR CNRS 7502, IECL, Université de Lorraine, site de Metz, Département de Mathématiques, UFR MIM, Ile du Saulcy, CS 50128, 57045 Metz Cedex 01, France

Identyfikatory

DOI

10.4064/cm6221-1-2016