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arXiv · 2406.11479

A proof of Sugawara's conjecture on Hasse-Weber ray class invariants

Patrick Morton
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Abstract

In this paper a proof is given of Sugawara's conjecture from 1936, that the ray class field of conductor $\mathfrak{f}$ over an imaginary quadratic field $K$ is generated over $K$ by a single primitive $\mathfrak{f}$-division value of the $\tau$-function, first defined by Weber and then modified by Hasse in his 1927 paper giving a new foundation of complex multiplication.

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Patrick Morton. 2024-06-17. A proof of Sugawara's conjecture on Hasse-Weber ray class invariants. https://arxiv.org/abs/2406.11479

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