Continued fractions, special values of the double sine function, and Stark units over real quadratic fields

DOI10.1016/j.jnt.2006.09.011zbMath1150.11041OpenAlexW1967491534MaRDI QIDQ880055

Brett A. Tangedal

Publication date: 10 May 2007

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jnt.2006.09.011

zbMATH Keywords

quadratic fieldsclass field theorydouble sine functionStark's conjecturezeta functions of number fields

Mathematics Subject Classification ID

Quadratic extensions (11R11) Class field theory (11R37) Zeta functions and (L)-functions of number fields (11R42)

Related Items (4)

On Shintani's ray class invariant for totally real number fields ⋮ Explicit computation of Gross-Stark units over real quadratic fields ⋮ On \(p\)-adic multiple zeta and log gamma functions ⋮ A two-variable generalization of the Kummer-Malmstén formula for the logarithm of the double gamma and double sine functions

Uses Software

• PARI/GP

Cites Work

• Two cases of Stark's conjecture
• Über die Werte der Dedekindschen Zetafunktion
• The Stark conjectures on Artin \(L\)-functions at \(s=0\). Lecture notes of a course in Orsay edited by Dominique Bernardi and Norbert Schappacher.
• Brumer elements over a real quadratic base field
• \(L\)-functions at \(s=1\). IV: First derivatives at \(s=0\)
• Generalized eta-functions and certain ray class invariants of real quadratic fields
• \(L\)-functions at \(s=1\). III: Totally real fields and Hilbert's twelfth problem
• On certain ray class invariants of real quadratic fields
• Stark's conjecture in multi-quadratic extensions, revisited.
• Hilbert’s twelfth problem and 𝐿-series
• Computing Stark units for totally real cubic fields
• Multiple sine functions
• Stark's conjecture over complex cubic number fields
• Computing the Hilbert class field of real quadratic fields
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