The addition theorem of Weierstrass's sigma function
Article
Received:
- 132 Downloads
- 7 Citations
Mathematics Subject Classification (1991)
39B32 33E05Preview
Unable to display preview. Download preview PDF.
References
- [Acz]Aczél, J.: The state of the second part of Hilbert's fifth problem. Bull. Am. Math. Soc.20, 153–163 (1989)Google Scholar
- [A-D]Aczél, J., Dhombres, J.: Functional equations in several variables. Cambridge: Cambridge University Press 1989Google Scholar
- [Bo1]Bonk, M.: On the second part of Hilbert's fifth problem. Math. Z.210, 475–493 (1992)Google Scholar
- [Bo2]Bonk, M.: The characterization of theta functions by functional equations. Habilitationsschrift, Braunschweig (unpublished, 1991)Google Scholar
- [Bur]Burckel, R.B.: An introduction to classical complex analysis. Boston, Basel Stuttgart: Birkhäuser 1979Google Scholar
- [Des]Deslisle, A.: Bestimmung der allgemeinsten der Funktionalgleichung der σ-Funktion genügenden Funktion. Math. Ann.30, 91–119 (1887)Google Scholar
- [Die]Dieudonné, J.: Foundations of modern analysis. New York: Academic Press 1969Google Scholar
- [Han]Hancock, H.: Lectures on the theory of elliptic functions. New York: Dover 1958Google Scholar
- [Har]Haruki, H.: Studies on certain functional equations from the standpoint of analytic function theory. Sci. Rep. Osaka Univ.14, 1–40 (1965)Google Scholar
- [Hur]Hurwitz, A.: Über die Weierstrass'sche σ-Funktion, pp. 133–141. Berlin 1914 In: Ges. Abh., Bd. 2, pp. 722–730. Boston Basel Stuttgart: Birkhäuser 1932Google Scholar
- [Igu]Igusa, J.: Theta functions. Berlin Heidelberg New York: Springer 1972Google Scholar
- [Kra]Krazer, A.: Lehrbuch der Thetafunktionen. Leipzig: Teubner 1903Google Scholar
- [Nev]Nevanlinna, R.: Eindeutige analytische Funktionen, 2. Aufl. Berlin Heidelberg New York: Springer 1953Google Scholar
- [R-R]Rochberg, R., Rubel, L.A.: A functional equation. Indiana Univ. Math. J.41, 363–376 (1992)Google Scholar
- [S-W]Stein, E.M., Weiss, G.: Introduction to Fourier analysis on Euclidean spaces. Princeton: Princeton University Press 1971Google Scholar
- [V-D]Van Vleck, E.B., H'Doubler, F.: A study of certain functional equations for the ϑ, Trans. Amer. Math. Soc.17, 9–49 (1916)Google Scholar
- [Wei]Weierstraß, K.: Zur Theorie der Jacobischen Funktionen von mehreren Veränderlichen. Sitzungsber Königl. Preuss. Akad. Wiss. 505 508 (1882); In: Werke, Bd. 3, pp. 155–159. Berlin: Mayer & Müller 1903Google Scholar
Copyright information
© Springer-Verlag 1994