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 language | English |
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Pages (from-to) | 176-224 |
Number of pages | 49 |
Journal | Canadian Journal of Mathematics |
Volume | 51 |
Issue number | 1 |
DOIs | |
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