Values of the Dedekind eta function at quadratic irrationalities

Alfred Van Der Poorten; Kenneth S. Williams

doi:10.4153/CJM-1999-011-1

Values of the Dedekind eta function at quadratic irrationalities

Alfred Van Der Poorten^*, Kenneth S. Williams

^*Corresponding author for this work

Macquarie University Administration Unit

Research output: Contribution to journal › Article › peer-review

16 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) = e^πiz/12∏^∞ _m=1(1 - e^2πimz) (im(z) > 0) (im(z) > 0).

Original language	English
Pages (from-to)	176-224
Number of pages	49
Journal	Canadian Journal of Mathematics
Volume	51
Issue number	1
DOIs	https://doi.org/10.4153/CJM-1999-011-1
Publication status	Published - 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

Access to Document

10.4153/CJM-1999-011-1

Cite this

@article{db60ee72f75943b18eaaed5dbd06488a,

title = "Values of the Dedekind eta function at quadratic irrationalities",

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).",

keywords = "Binary quadratic forms, Dedekind eta function, Form class group, Quadratic irrationalities",

author = "\{Van Der Poorten\}, Alfred and Williams, \{Kenneth S.\}",

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",

year = "1999",

month = feb,

doi = "10.4153/CJM-1999-011-1",

language = "English",

volume = "51",

pages = "176--224",

journal = "Canadian Journal of Mathematics",

issn = "0008-414X",

publisher = "Cambridge University Press (CUP)",

number = "1",

}

TY - JOUR

T1 - Values of the Dedekind eta function at quadratic irrationalities

AU - Van Der Poorten, Alfred

AU - Williams, Kenneth S.

N1 - 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

PY - 1999/2

Y1 - 1999/2

N2 - 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).

AB - 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).

KW - Binary quadratic forms

KW - Dedekind eta function

KW - Form class group

KW - Quadratic irrationalities

UR - https://www.scopus.com/pages/publications/0033435075

UR - http://dx.doi.org/10.4153/CJM-2001-018-8

U2 - 10.4153/CJM-1999-011-1

DO - 10.4153/CJM-1999-011-1

M3 - Article

AN - SCOPUS:0033435075

SN - 0008-414X

VL - 51

SP - 176

EP - 224

JO - Canadian Journal of Mathematics

JF - Canadian Journal of Mathematics

IS - 1

ER -

Values of the Dedekind eta function at quadratic irrationalities

Abstract

Bibliographical note

Keywords

Access to Document

Other files and links

Fingerprint

Cite this