Values of the Dedekind eta function at quadratic irrationalities

Alfred Van Der Poorten*, Kenneth S. Williams

*Corresponding author for this work

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

Let d be the discriminant of an imaginary quadratic field. Let a, b, c be integers such that b2 - 4ac = d, a > 0, gcd(a,b,c) = 1. The value of /η ((b + √d)/2a) |is determined explicitly, where η(z) is Dedekind's eta function η(z) = eπiz/12 m=1(1 - e2πimz) (im(z) > 0) (im(z) > 0).

Original languageEnglish
Pages (from-to)176-224
Number of pages49
JournalCanadian Journal of Mathematics
Volume51
Issue number1
DOIs
Publication statusPublished - Feb 1999

Bibliographical note

Corrigendum can be found in Canadian Journal of Mathematics, 53(2001), pp. 434-448, 2001.
http://dx.doi.org/10.4153/CJM-2001-018-8

Keywords

  • Binary quadratic forms
  • Dedekind eta function
  • Form class group
  • Quadratic irrationalities

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