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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.
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참고문헌 (16)
참고문헌 신청
D. A. Cox / 1989 / Primes of the form $x^2+ny^2$ : Fermat, Class Field, and Complex Multiplication / John Wiley & Sons, Inc.
I. S. Eum / 2016 / Ring class invariants over imaginary quadratic fields / Forum Math. 28(2):201~217
G. J. Janusz / 1996 / Algebraic Number Fields / Amer. Math. Soc
H. Y. Jung / 2011 / Ray class invariants over imaginary quadratic fields / Tohoku Math. J. 63(3):413~426
J. K. Koo / 2010 / Function fields of certain arithmetic curves and application / Acta Arith. 141(4):321~334
I. S. Eum / 2016 / Ring class invariants over imaginary quadratic fields / Forum Math. 28(2):201~217
G. J. Janusz / 1996 / Algebraic Number Fields / Amer. Math. Soc
H. Y. Jung / 2011 / Ray class invariants over imaginary quadratic fields / Tohoku Math. J. 63(3):413~426
J. K. Koo / 2010 / Function fields of certain arithmetic curves and application / Acta Arith. 141(4):321~334
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