Patrick Morton

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20242026

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math.NT2026

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

Patrick Morton

In this paper a proof is given of Sugawara's conjecture from 1936, that the ray class field of conductor $f$ over an imaginary quadratic field $K$ is generated over $K$ …

math.NT2025

Algebraic functions and class number formulas

Sushmanth J. Akkarapakam, Patrick Morton

A class number formula is proved for extended ring class fields $L_{O, 9}$ over imaginary quadratic fields $K_{d} = Q (- d)$ , in which the prime $p = 3$ splits…

math.NT2024

On Ramanujan's cubic continued fraction

Sushmanth J. Akkarapakam, Patrick Morton

The periodic points of the algebraic function defined by the equation $g (x, y) = x^{3} (4 y^{2} + 2 y + 1) - y (y^{2} - y + 1)$ are shown to be expressible in terms of Ramanujan's cubic continued fract…