Algebraic independence results for the values of the theta-constants and some identities

Carsten Elsner, Masanobu Kaneko, Yohei Tachiya

研究成果: Contribution to journalArticle査読

1 被引用数 (Scopus)

抄録

In the present work, we give algebraic independence results for the values of the classical theta-constants ϑ2(τ), ϑ3(τ), and ϑ4(τ). For example, the two values ϑα(mτ) and ϑβ(nτ) are algebraically independent over Q for any τ in the upper half-plane when eπiτ is an algebraic number, where m, n ≥ 1 are integers and α, β ∈ {2, 3, 4} with (m, α) ≠ (n, β). This algebraic independence result provides new examples of transcendental numbers through some identities found by S. Ramanujan. We additionally give some explicit identities among the three theta-constants in particular cases.

本文言語英語
ページ(範囲)71-80
ページ数10
ジャーナルJournal of the Ramanujan Mathematical Society
35
1
出版ステータス出版済み - 3 2020

All Science Journal Classification (ASJC) codes

  • 数学 (全般)

フィンガープリント

「Algebraic independence results for the values of the theta-constants and some identities」の研究トピックを掘り下げます。これらがまとまってユニークなフィンガープリントを構成します。

引用スタイル