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arXiv · 1608.06705

On a problem of Hasse and Ramachandra

Ja Kyung Koo·Dong Hwa Shin·Dong Sung Yoon
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Abstract

Let $K$ be an imaginary quadratic field, and let $\mathfrak{f}$ be a nontrivial integral ideal of $K$. Hasse and Ramachandra asked whether the ray class field of $K$ modulo $\mathfrak{f}$ can be generated by a single value of the Weber function. We completely resolve this question when $\mathfrak{f}=(N)$ for an integer $N>1$.

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Ja Kyung Koo, Dong Hwa Shin, Dong Sung Yoon. 2016-08-24. On a problem of Hasse and Ramachandra. https://arxiv.org/abs/1608.06705

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