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).

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Keywords Binary quadratic forms, Dedekind eta function, Form class group, Quadratic irrationalities
Journal Canadian Journal of Mathematics
Van Der Poorten, A. (Alfred), & Williams, K.S. (1999). Values of the Dedekind eta function at quadratic irrationalities. Canadian Journal of Mathematics, 51(1), 176–224.