The Chowla-Selberg formula for genera

• Autorzy: James G. Huard , Pierre Kaplan , Kenneth S. Williams
• Języki publikacji: EN
• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1995
• Tom: 73
• Numer: 3
• Strony: 271-301

Daty

wydano

1995

otrzymano

1994-12-29

Twórcy

autor

James G. Huard

• Department of Mathematics, Canisius College, Buffalo, New York 14208, U.S.A.

autor

Pierre Kaplan

• Département de Mathématiques, Université de Nancy 1, B.P. 239, 54506 Vandoeuvre les Nancy Cedex, France

autor

Kenneth S. Williams

• Centre for Research in Algebra and Number Theory, Department of Mathematics and Statistics, Carleton University, Ottawa, Ontario, Canada KIS 5B6

Bibliografia

• [1] J. M. Borwein and P. B. Borwein, Pi and the AGM, Wiley, New York, 1987.
• [2] D. A. Buell, Binary Quadratic Forms, Springer, New York, 1989.
• [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 $f_i$ 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.