논문KCI 등재
ON SOME THETA CONSTANTS AND CLASS FIELDS
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We first find a sufficient condition for a product of theta constants to be a Siegel modular function of a given even level. And, when K (2p) denotes the ray class field of K = Q(e 2πi/5 ) modulo 2p for an odd prime p, we describe a subfield of K (2p) generated by the special value of a certain theta constant by using Shimura’s reciprocity law.
Abstract
We first find a sufficient condition for a product of theta constants to be a Siegel modular function of a given even level. And, when K (2p) denotes the ray class field of K = Q(e 2πi/5 ) modulo 2p for an odd prime p, we describe a subfield of K (2p) generated by the special value of a certain theta constant by using Shimura’s reciprocity law.
참고문헌 (12)
- E. de Shalit, "special values of theta functions of genus two", Ann. Inst. Fourier (Grenoble), 47(3), pp.775~799 (1997)
- J.-I. Igusa, "On the graded ring of theta-constants. II", Amer. J. Math, 88(1), pp.221~236 (1966)
- H. Y. Jung, "Ray class invariants over imaginary quadratic fields", Tohoku Math. J, 63(3), pp.413~426 (2011)
- H. Klingen, "Introductory Lectures on Siegel Modular Forms" (1990), Cambridge University Press
- K. Komatsu, "Construction of a normal basis by special values of Siegel modular functions", Proc. Amer. Math. Soc, 128(2), pp.315~323 (2000)
- D. Kubert, "Modular Units" (1981), Spinger-Verlag
- S. Lang, "Elliptic Functions" (1987), Spinger-Verlag
- G. Shimura, "On canonical models of arithmetic quotients of bounded symmetric domains", Ann. of Math, 91, pp.144~222 (1970)
- G. Shimura, "Introduction to the Arithmetic Theory of Automorphic Functions" (1971), Iwanami Shoten and Princeton University Press
- G. Shimura, "Theta functions with complex multiplication", Duke Math. J, 43(4), pp.673~696 (1976)
- G. Shimura, "On certain reciprocity-laws for theta functions and modular forms", Acta Math, 141(1-2), pp.35~71 (1978)
- G. Shimura, "Abelian Varieties with Complex Multiplication and Modular Functions" (1998), Princeton University Press
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