References  pp. 378-382


By J. V. Armitage and W. F. Eberlein
Abel, N. H., 1881, Oeuvres Complètes, 2 vols., Christiana, Gr⊘ndahl and Son.
Agnew, R. P., 1960, Differential Equations, second edn., New York, McGraw-Hill.
Ahlfors, L. V., 1979, Complex Analysis, third edn., New York, McGraw-Hill.
Apostol, T. M., 1969, Mathematical Analysis, Reading, Mass, Addison-Wesley.
Appell, P., 1878, Sur une interprétation des valeurs imaginaires du temp en mécanique, C. R. Acad. Sci. Paris, 87, 1074–1077.
Baker, H. F., 1992, Principles of Geometry, 6 vols., Cambridge, Cambridge University Press.
Bateman, H., 1953, Higher Transcendental Functions, 3 vols., (eds. Erdélyi, Magnus, Oberhettinger and Tricomi) New York, McGraw-Hill.
Beardon, A. F., 1991, Iteration of Rational Functions, Graduate texts in Mathematics, 132, Section 4.3, New York, Springer.
Biane, P., Pitman, J. and Yor, M., 2001, Probability laws related to the Jacobi theta and Riemann zeta functions, and Brownian excursions, Bulletin American Math. Soc., 38, 435–465.
Birch, B. J. and Swinnerton-Dyer, H. P. F., 1965, Notes on elliptic curves, II, J. Reive Angew. Math., 218, 79–108.
Bowman, F., 1961, Introduction to Elliptic Functions with Applications, New York, Dover.
Briot, C. and Bouquet, J. C., 1875, Théorie des fonctions élliptiques, Paris, Gauthier Villars.
Burnside, W. S. and Panton, A. W., 1901, Theory of Equations (especially Vol. II) Dublin, Dublin University Press.
Cassels, J. W. S., 1991, Lectures on Elliptic Curves, London Mathematical Society Student Texts, 24, Cambridge, Cambridge University Press.
Cayley, A., 1895, An Elementary Treatise on Elliptic Functions, London, George Bell and Sons.
Coddington, E. A. and Levinson, N., 1955, Theory of Differential Equations, New York, McGraw-Hill.
Coddington, E. A., 1961, An Introduction to Ordinary Differential Equations, Englewood Cliffs, N. J., Prentice-Hall.
Copson, E. T., 1935, An Introduction to the Theory of Functions of a Complex Variable, Oxford, Oxford University Press.
Cornell, G., Silverman, J. H. and Stevens, G., 1997, Modular Forms and Fermat's Last Theorem, Berlin, Springer.
Courant, R. and Hilbert, D., 1968, Methoden der mathematischen Physik, 2 Vols., Berlin, Springer.
Cox, D. A., 1984, The Arithmetic-Geometric Mean of Gauss, L'Enseig. Math., 30, 275–330.
Coxeter, H. S. M., 1961, Introduction to Geometry, New York and London, Wiley, (second edn., 1969).
Davenport, H., 1952, The Higher Arithmetic, Hutchinson's, University Library, London, Hutchinson.
Dickson, L. E., 1934, History of the Theory of Numbers (especially Vol. 2, Chapter 9), New York, G. E. Stechert & Co.
du Val, P., 1973, Elliptic Functions and Elliptic Curves, London Mathematical Society Lecture Note Series, 9, Cambridge, Cambridge University Press.
Durell, C. V., 1948, Projective Geometry, London, Macmillan.
Dutta, M. and Debnath, L., 1965, Elements of the Theory of Elliptic and Associated Functions with Applications, Calcutta, The World Press Private Ltd.
Dym, H. and McKean, H. P., 1972, Fourier Series and Integrals, New York and London, Academic Press.
Eberlein, W. F. 1966, The Circular Function(s), Math. Mag., 39, 197–201.
Eberlein, W. F., 1954, The Elementary Transcendental Functions, Amer. Math. Monthly, 61, 386–392.
Erdos, P., 2000, Spiraling the earth with C. G. J. Jacobi, American Journal of Physics, 68 (10), 888–895.
Evelyn, C. J. A., Money-Coutts, G. B. and Tyrrell, J. A., 1974, The Seven Circles Theorem and Other New Theorems, London, Stacey International.
Faltings, G., 1995, The proof of Fermat's Last Theorem by R. Taylor and A. Wiles, Not. Amer. Math. Soc., 42, No.7, 743–746.
Fuchs, L., 1870, Die Periodicitäz moduln der hyperelliptischen Integrale als Funktionen eines Parameters aufgefasst, J. reine angew. Math., 71, 91–136.
Gauss, C. F. 1801, Disquisitiones Arithmeticae, Leipzig, Fleischer, reprinted by Impression Anastaltique, Culture et Civilisation, Bruxelles, 1968. English translation by A. A. Clarke, Yace University Press, 1966. Also in Gauss, C. F., 1870, Werke, I, Leipzig, Teubner.
Gauss, C. F., 1799, Arithmetisch Geometrisches Mittel, Werke III, 361–432.
Glaisher, J. W. L. 1882, Systems of formulae in elliptic functions, Messenger of Mathematics, Ⅺ, 86.
Glaisher, J. W. L., 1881, On some elliptic functions and trigonometrical theorems, Messenger of Mathematics, X, 92–97.
Glaisher, J. W. L., 1907, On the representation of a number as the sum of two, four, six, eight, ten and twelve squares, Quart. J. Pure Appl. Math., XXXVIII, 1–62.
Green, M. B. Schwarz, J. M. and Witten, E., 1987, Superstring Theory, Cambridge, Cambridge University Press.
Greenhill, A. G., 1892, The Applications of Elliptic Functions, London, Macmillan.
Grosswald, E., 1984, Representations of Integers as Sums of Squares, New York, Springer-Verlag.
Halphen, G. H., 1886–91, Traité des fonctions élliptiques et de leurs applications, 3 vols., Paris, Gauthier-Villars.
Hancock, H., 1958, Lectures on the Theory of Elliptic Functions, New York, Dover.
Hardy, G. H. and Wright, E. M., 1979, An Introduction to the Theory of Numbers, fifth edn., Oxford, Oxford University Press.
Hardy, G. H., 1944, A Course of Pure Mathematics, Cambridge, Cambridge University Press.
Hermite, C. 1861, Lettre addressée à M. Liouville, Theorie des Fonctions Elliptiques et ses Applications Arithmétiques, Comptes Rendees LIII; Oeuvres, 109–124.
Hermite, C., 1862, Sur les theorems de M. Kronecker relatifs aux formes quadratiques, Comptes Rendus de l'Academie des Sciences, LV, 11–85, (See Oeuvres, II, Paris, Gauthier-Villars, 1908, pp. 241–263.)
Hurwitz, A. and Courant, R., 1964, Vorlesungen über allgemeine Funktionentheorie und elliptische Funktionen, Berlin, Springer.
Jacobi, C. G. J. 1835, Journal für Math., XIII, 54–56; Gesammelte Werke, II, (1882), 25–26.
Jacobi, C. G. J. 1838, Theorie der elliptischen Funktionen aus der Eigenschaften der Thetareihen abgeleitet, Gesammelte Werke, I, (1882), 497–538.
Jacobi, C. G. J., 1829, Fundamenta Nova Theoriae Functionarum Ellipticarum, reprinted in Gesammelte Werke, I, (1882), 49–239.
Jones, G. A. and Singerman, D., 1987, Complex Functions, Cambridge, Cambridge University Press.
Jordan, M. C., 1893, Cours d'analyse de l'Ecole Polytechnique, Paris, Gauthier-Villars.
Kendall, M. G., 1941, Correlation and elliptic functions, J. Royal Statistical Society, 104, 281–283.
Klein, F. and Fricke, R., 1890, Vorlesungen über die Theorie der elliptischen Modulfunctionen, Leipzig, Teubner.
Klein, F., 1884, Vorlesungen über das Ikosaeder und die Auflösung der Gleichungen von fünften Grade, Leipzig, Teubner; English translation, The Icosahedron and the Solution of Equations of the Fifth Degree, trans. G. G. Morrice, New York, Dover.
Knopp, M., 1970, Modular Forms in Analytic Number Theory, Chicago, Markham.
Koblitz, N., 1991, A Course in Number Theory and Cryptography, New York, Berlin and Heidelberg, Springer.
Kronecker, L., 1860, Über die Anzahl der verschiedenen Classen quadratische Formen von negative Determinante, J. reine. angew. Math. 57; (reprinted in Werke (1895–1931), 5 vols., Leipzig, Teubner, 248–255, reprinted New York, Chelsea, 1968.)
Landau, E., 1947, Vorlesungen über Zahlentheorie, Part 1, Chelsea reprint, New York, Chelsea, 114–125.
Lang, S., 1987, Elliptic Functions, second edn., Berlin, Springer.
Lawden, D. F., 1989, Elliptic Functions and Applications, Applied Mathematical Sciences, vol. 80, New York, Springer-Verlag.
Lord Rayleigh, 1929, The Theory of Sound, 2 vols., second edn., London, Macmillan.
Lowan, A. N., Blanch, G. and Horenstein, W., 1942, On the inversion of the q-series associated with Jacobian elliptic functions, Bull. Amer. Math. Soc., 48, 737–738.
McKean, H. and Moll, V., 1997, Elliptic Curves, Function Theory, Geometry, Arithmetic, Cambridge, Cambridge University Press.
Nevanlinna, R. and Paatero, V., 1969, Introduction to Complex Analysis (tr. T. Kövari and G. S. Goodman), Reading, Mass, Addison-Wesley.
Neville, E. H., 1944, The Jacobian elliptic functions, Oxford, Oxford University Press.
Newboult, H. O., 1946, Analytical Methods in Dynamics, Oxford, Oxford University Press.
Ore, O., 1957, Niels Henrik Abel: Mathematician Extraordinary, Minneapolis, University of Minnesota Press.
Osgood, W. F., 1935, Advanced Calculus, New York, Macmillan.
Polya, G. 1927, Elementarer Beweis einer Thetaformel, Sitz. der Phys. Math. Klasse, 158–161, Berlin, Preuss. Akad. der Wiss. Reprinted in Collected Papers, Vol. 1, 303–306, Cambridge, Mass MIT Press, 1974–84.
Polya, G. 1954, Induction and Analogy in Mathematics and Patterns of Plausible Inference (2 vols.), New Jersey, Princeton.
Polya, G., 1921, Über eine Aufgabe der Wahrscheinlichkeitsrechnung betreffend die Irrfahrt im Strassennetz, Math. Ann., 84,149–60. Reprinted in Collected Papers, vol. 4, 69–80, Cambridge, Mass, MIT Press, 1974–84.
Prasolov, V. and Solovyev, Y., 1997, Elliptic Functions and Elliptic Integrals, Translations of Mathematical Monographs, Vol. 170, Providence, Rhode Island, American Mathematical Society.
Rademacher, H., 1973, Topics in Analytic Number Theory, Berlin, Springer.
Rigby, J. F., 1981, On the Money-Coutts configuration of 9 anti-tangent cycles, Proc. London Mathematical Society, 43, (1), 110–132.
Serre, J.-P., 1970, Cours d'Arithmétique, Paris, Presses Universitaires de France. (English translation, 1973, A Course in Arithmetic, GTM 7, Berlin, Springer-Verlag.)
Siegel, C. L., 1969, Topics in Complex Function Theory, Vol. 1, New York, Wiley-Interscience.
Smith, H. J. S., 1965, Report on the Theory of Numbers, New York, Chelsea.
Stewart, I. N., 2003, Galois Theory, third edn. Buca Raton, Florida, Chapman and Hall, CRC Press.
Tannery J. and Molk, J. 1939, The Theory of Functions, Oxford, Oxford University Press.
Tannery J. and Molk, J., 1893–1902, Elements de la théorie des Functions Elliptiques, 4 vols., Paris, Gauthier-Villars. Reprinted New York, Chelsea, 1972.
Titchmarsh, E. C., 1986, The Theory of the Riemann Zeta-functions, revised by D. R. Heath-Brown, Oxford, Oxford University Press.
Tyrrell, J. A. and Powell, M. T., 1971, A theorem in circle geometry, Bull. London Mathematical Society, 3, 70–74.
Watson, G. N. 1944, A Treatise on the Theory of Bessel Functions, Cambridge, Cambridge University Press.
Watson, G. N., 1939, Three triple integrals, Oxford Quart. J. Math., 10, 266–276.
Weber, H. 1908, Lehrbuch der Algebra (especially Vol. 3), second edn. Braunschweig, Vieweg. Reprinted New York, Chelsea, 1961.
Weierstrass, K., 1883, Zur Theorie der elliptischen Funktionen, Sitzungberichte der Akadamie des Wissenschaften zu Berlin, 193–203. (Math. Werke, 2, 1895, 257–309) Berlin, Mayer and Müller.
Weil, A., 1975, Elliptic Functions according to Eisenstein and Kronecker, Berlin, Springer.
Whittaker, E. T., 1937, A Treatise on the Analytical Dynamics of Particles and Rigid Bodies, fourth edn., Cambridge, Cambridge University Press.
Whittaker, E. T., and Watson, G. N., 1927, A Course of Modern Analysis, fourth edn., Cambridge, Cambridge University Press.
Williams, D., 2001, Weighing the Odds – a Course in Probability and Statistics, Cambridge, Cambridge University Press.
Zagier, D., 1991, The Birch–Swinnerton-Dyer conjecture from a naïve point of view, Prog. Math., 89, 377–389.