본문 바로가기
KERD
논문KCI 등재

Generation of ring class fields by eta-quotients

2

조회

0

다운로드

0

인용

0

참고문헌

키워드

주제분류수학

초록

We generate ring class fields of imaginary quadratic fields in terms of the special values of certain eta-quotients, which are related to the relative norms of Siegel-Ramachandra invariants. These give us minimal polynomials with relatively small coefficients from which we are able to solve certain quadratic Diophantine equations concerning non-convenient numbers.

Abstract

We generate ring class fields of imaginary quadratic fields in terms of the special values of certain eta-quotients, which are related to the relative norms of Siegel-Ramachandra invariants. These give us minimal polynomials with relatively small coefficients from which we are able to solve certain quadratic Diophantine equations concerning non-convenient numbers.

참고문헌 (16)

  1. TEX>: Fermat, Class Field, and Complex Multiplication, "Primes of the form <TEX>$x^2+ny^2$<", pp.1989, D. A. Cox
  2. I. S. Eum, "Ring class invariants over imaginary quadratic fields", Forum Math., 28(2), pp.201~217 (2016)
  3. G. J. Janusz, "Algebraic Number Fields" (1996), Amer. Math. Soc
  4. H. Y. Jung, "Ray class invariants over imaginary quadratic fields", Tohoku Math. J., 63(3), pp.413~426 (2011)[DOI]
  5. J. K. Koo, "Function fields of certain arithmetic curves and application", Acta Arith., 141(4), pp.321~334 (2010)[DOI]
  6. J. K. Koo, "On some arithmetic properties of Siegel functions", Math. Z., 264(1), pp.137~177 (2010)[DOI]
  7. D. Kubert, "Modular Units, Grundlehren der mathematischen Wissenschaften 244" (1981), Spinger-Verlag
  8. S. Lang, "Elliptic Functions, With an appendix by J. Tate" (1987), Spinger-Verlag
  9. K. Ono, "The Web of Modularity: Arithmetic of the Coeffcients of Modular Forms and q-series", CBMS Regional Conf. Series in Math., 102 (2004), Amer. Math. Soc.
  10. K. Ramachandra, "Some applications of Kronecker's limit formula", Ann. of Math., 80, pp.104~148 (1964)[DOI]
  11. R. Schertz, "Construction of ray class fields by elliptic units", J. Theor. Nombres Bordeaux, 9(2), pp.383~394 (1997)[DOI]
  12. J.-P. Serre, "A Course in Arithmetic, Grad. texts in Math." (1973), Springer-Verlag
  13. G. Shimura, "Introduction to the Arithmetic Theory of Automorphic Functions" (1971), Iwanami Shoten and Princeton University Press
  14. P. Stevenhagen, "Hilbert's 12th problem, complex multiplication and Shimura reciprocity, Class Field Theory-Its Centenary and Prospect (Tokyo, 1998), Adv. Stud. Pure Math. 30", pp.161~176 (2001)
  15. A.Weil, "Number Theory: An Approach Through History; From Hammurapi to Legendre" (1984), Birkhauser Boston, Inc.
  16. P. J. Weinberger, "Exponents of the class groups of complex quadratic fields", Acta Arith., 22, pp.117~124 (1973)[DOI]

관련 논문AI추천

이 간행물의 다른 논문 (14건)