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

Patrick Morton

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

Number Theory 2025-03-12 v4

Authors: Patrick Morton

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.

Keywords

Sugawara's conjecture ray class field complex multiplication tau-function imaginary quadratic field Hasse-Weber ray class invariant

Cite

@article{arxiv.2406.11479,
  title  = {A proof of Sugawara's conjecture on Hasse-Weber ray class invariants},
  author = {Patrick Morton},
  journal= {arXiv preprint arXiv:2406.11479},
  year   = {2025}
}

Comments

75 pages; an additional case of the conjecture has now been included in Section 6.2

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

Abstract

Keywords

Cite

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