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Generation of ray class fields modulo 2, 3, 4 or 6 by using the Weber function

신동화|구자경|정호윤
대한수학회 (The Korean Mathematical Society)|2018.03|대한수학회지 (Journal of the KMS)|제55권 제2호|pp. 343-372

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참고문헌

키워드

complex multiplicationclass field theoryWeber function
주제분류수학

초록

Let $K$ be an imaginary quadratic field with ring of integers $\mathcal{O}_K$. Let $E$ be an elliptic curve with complex multiplication by $\mathcal{O}_K$, and let $h_E$ be the Weber function on $E$. Let $N\in\{2,\,3,\,4,\,6\}$. We show that $h_E$ alone when evaluated at a certain $N$-torsion point on $E$ generates the ray class field of $K$ modulo $N\mathcal{O}_K$. This would be a partial answer to the question raised by Hasse and Ramachandra.

Abstract

Let $K$ be an imaginary quadratic field with ring of integers $\mathcal{O}_K$. Let $E$ be an elliptic curve with complex multiplication by $\mathcal{O}_K$, and let $h_E$ be the Weber function on $E$. Let $N\in\{2,\,3,\,4,\,6\}$. We show that $h_E$ alone when evaluated at a certain $N$-torsion point on $E$ generates the ray class field of $K$ modulo $N\mathcal{O}_K$. This would be a partial answer to the question raised by Hasse and Ramachandra.

참고문헌 (24)

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