|
Continued fractions and modular functions
Author:
W. Duke
Journal:
Bull. Amer. Math. Soc. 42 (2005), 137-162
MSC (2000):
Primary 11Fxx, 11Gxx
Posted:
January 25, 2005
MathSciNet review:
2133308
Full-text PDF
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Additional Information
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- A. Folsom, Modular forms and Eisenstein's continued fractions. Preprint, 2004.
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- R. Fricke, Lehrbuch der Algebra, Band 2, Vieweg, Braunschweig, 1926.
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- B. Gordon, Some continued fractions of the Rogers-Ramanujan type. Duke Math. J. 32 (1965), 741-748. MR 0184001 (32:1477)
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- G. H. Hardy, Ramanujan: twelve lectures on subjects suggested by his life and work. Chelsea Publishing Company, New York, 1959. MR 0106147 (21:4881)
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- F. Klein, Weitere Untersuchungen über das Ikosaeder. Math. Ann. 12, 509-561 (1877) [in Gesammelte Math. Abhandlungen II , 321-384, Springer, 1922].
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- T. Muir, On Eisenstein's continued fractions, Transactions of the Royal Society of Edinburgh, 28 (1876-1878), 135-144.
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- K. G. Ramanathan, On Ramanujan's continued fraction. Acta Arith. 43 (1984), no. 3, 209-226. MR 0738134 (85d:11012)
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- Th. Schneider, Arithmetische Untersuchungen elliptischer Integrale, Math. Ann. 113, 1-13 (1937).
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. Comment. Math. Helv. 59 (1984), no. 4, 651-676 [#131 in Collected papers, Volume III, Springer-Verlag, New York, 1985]. MR 0780081 (86k:11067)
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- J. J. Sylvester, On a remarkable modification of Sturm's theorem. Philosophical Magazine 4, 446-457 (1853) [#61 in Collected Math. Papers, Vol. I, 609-619, Chelsea, New York, 1973].
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- G. Toth, Finite Möbius groups, minimal immersions of spheres, and moduli. Universitext, Springer-Verlag, New York, 2002. MR 1863996 (2002i:53082)
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- G. N. Watson, Theorems stated by Ramanujan (VII): Theorems on continued fractions, J. London Math. Soc. 4 (1929), 39-48.
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- G. N. Watson, Theorems stated by Ramanujan (IX): Two continued fractions, J. London Math. Soc. 4 (1929), 231-237.
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- H. Weber, Lehrbuch der Algebra, III. Braunschweig, 1908 [reprinted by Chelsea, New York, 1961].
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Additional Information
W. Duke
Affiliation:
Department of Mathematics, University of California, Box 951555, Los Angeles, California 90095-1555
Email:
wdduke@ucla.edu
DOI:
http://dx.doi.org/10.1090/S0273-0979-05-01047-5
PII:
S 0273-0979(05)01047-5
Received by editor(s):
November 4, 2003
Posted:
January 25, 2005
Additional Notes:
Research supported in part by NSF Grant DMS-0355564.
Article copyright:
© Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
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