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ArticleOriginal scientific text

Title

The Chowla-Selberg formula for genera

Authors 1, 2, 3

Affiliations

  1. Department of Mathematics, Canisius College, Buffalo, New York 14208, U.S.A.
  2. Département de Mathématiques, Université de Nancy 1, B.P. 239, 54506 Vandoeuvre les Nancy Cedex, France
  3. Centre for Research in Algebra and Number Theory, Department of Mathematics and Statistics, Carleton University, Ottawa, Ontario, Canada KIS 5B6

Bibliography

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  3. H. Cohn, A Second Course in Number Theory, Wiley, New York, 1962.
  4. L. E. Dickson, Introduction to the Theory of Numbers, Dover, New York, 1957.
  5. P. G. L. Dirichlet, Vorlesungen über Zahlentheorie, Chelsea, New York, 1968.
  6. D. R. Estes and G. Pall, Spinor genera of binary quadratic forms, J. Number Theory 5 (1973), 421-432.
  7. K. Hardy and K. S. Williams, The class number of pairs of positive-definite binary quadratic forms, Acta Arith. 52 (1989), 103-117.
  8. M. Kaneko, A generalization of the Chowla-Selberg formula and the zeta functions of quadratic orders, Proc. Japan Acad. 66 (1990), 201-203.
  9. P. Kaplan and K. S. Williams, The Chowla-Selberg formula for non-fundamental discriminants, preprint, 1992.
  10. Y. Nakkajima and Y. Taguchi, A generalization of the Chowla-Selberg formula, J. Reine Angew. Math. 419 (1991), 119-124.
  11. A. Schinzel and U. Zannier, Distribution of solutions of diophantine equations f₁(x₁) f₂(x₂) = f₃(x₃), where fi are polynomials, Rend. Sem. Mat. Univ. Padova 87 (1992), 39-68.
  12. A. Selberg and S. Chowla, On Epstein's zeta-function, J. Reine Angew. Math. 227 (1967), 86-110.
  13. C. L. Siegel, Advanced Analytic Number Theory, Tata Institute of Fundamental Research, Bombay, 1980.
  14. G. Tenenbaum, Introduction à la théorie analytique et probabiliste des nombres, Institut Élie Cartan 13 (1990), Université de Nancy 1.
  15. H. Weber, Lehrbuch der Algebra, Vol. III, 3rd ed., Chelsea, New York, 1961.
  16. K. S. Williams and N.-Y. Zhang, The Chowla-Selberg relation for genera, preprint, 1993.
  17. I. J. Zucker, The evaluation in terms of Γ-functions of the periods of elliptic curves admitting complex multiplication, Math. Proc. Cambridge Philos. Soc. 82 (1977), 111-118.
Acta Arithmetica
1995/73/3
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Pages:
271-301
Main language of publication
English
Received
1994-12-29
Published
1995
Exact and natural sciences