Values of the Dedekind Eta Function at Quadratic Irrationalities

@inproceedings{Poorten1999ValuesOT,
  title={Values of the Dedekind Eta Function at Quadratic Irrationalities},
  author={Alfred J. van der Poorten and Kenneth S. Williams},
  year={1999}
}
Let d be the discriminant of an imaginary quadratic field. Let a, b, c be integers such that b − 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 ∞ ∏ m=1 (1− e) ( im(z) > 0 ) . 

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References

Publications referenced by this paper.
Showing 1-10 of 10 references

The Chowla-Selberg relation for genera

  • K. S. Williams, N.-Y. Zhang
  • Preprint
  • 1993
Highly Influential
6 Excerpts

The Chowla-Selberg formula for genera

  • J. G. Huard, P. Kaplan, K. S. Williams
  • Acta Arith. 73
  • 1995
Highly Influential
4 Excerpts

Advanced Number Theory

  • H. Cohn
  • Dover Publications, Inc., New York
  • 1980
Highly Influential
4 Excerpts

On a formula of Dirichlet

  • P. Kaplan, K. S. Williams
  • Far East J. Math. Sci. 5
  • 1997
1 Excerpt

Table of Integrals

  • I. S. Gradshteyn, I. M. Ryzhik
  • Series, and Products. Fifth Edition, Academic…
  • 1994
1 Excerpt

Elementary and Analytic Theory of Algebraic Numbers

  • W. Narkiewicz
  • Springer-Verlag, New York
  • 1990

Primes of the Form x2 + ny2

  • D. A. Cox
  • John Wiley and Sons, New York
  • 1989
3 Excerpts

Advanced Analytic Number Theory

  • C. L. Siegel
  • Tata Institute of Fundamental Research, Bombay
  • 1980

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