The Chowla-Selberg formula for genera
James G. Huard; Pierre Kaplan; Kenneth S. Williams
Acta Arithmetica (1995)
- Volume: 73, Issue: 3, page 271-301
- ISSN: 0065-1036
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topJames G. Huard, Pierre Kaplan, and Kenneth S. Williams. "The Chowla-Selberg formula for genera." Acta Arithmetica 73.3 (1995): 271-301. <http://eudml.org/doc/206821>.
@article{JamesG1995,
author = {James G. Huard, Pierre Kaplan, Kenneth S. Williams},
journal = {Acta Arithmetica},
keywords = {Chowla-Selberg formula for genera; class number; gamma function; binary quadratic forms with arbitrary discriminants},
language = {eng},
number = {3},
pages = {271-301},
title = {The Chowla-Selberg formula for genera},
url = {http://eudml.org/doc/206821},
volume = {73},
year = {1995},
}
TY - JOUR
AU - James G. Huard
AU - Pierre Kaplan
AU - Kenneth S. Williams
TI - The Chowla-Selberg formula for genera
JO - Acta Arithmetica
PY - 1995
VL - 73
IS - 3
SP - 271
EP - 301
LA - eng
KW - Chowla-Selberg formula for genera; class number; gamma function; binary quadratic forms with arbitrary discriminants
UR - http://eudml.org/doc/206821
ER -
References
top- [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. Zbl0084.26901
- [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. Zbl0268.10010
- [7] K. Hardy and K. S. Williams, The class number of pairs of positive-definite binary quadratic forms, Acta Arith. 52 (1989), 103-117. Zbl0687.10014
- [8] M. Kaneko, A generalization of the Chowla-Selberg formula and the zeta functions of quadratic orders, Proc. Japan Acad. 66 (1990), 201-203. Zbl0721.11046
- [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. Zbl0721.11045
- [11] A. Schinzel and U. Zannier, Distribution of solutions of diophantine equations f₁(x₁) f₂(x₂) = f₃(x₃), where 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. Zbl0166.05204
- [13] C. L. Siegel, Advanced Analytic Number Theory, Tata Institute of Fundamental Research, Bombay, 1980. Zbl0478.10001
- [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. Zbl0356.33003
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