Patrick Morton

activity

20142026

most citedSolutions of diophantine equations as periodic points of

p

-adic algebraic functions, II: The Rogers-Ramanujan continued fraction

5 citations · 33 across the 26 of their papers we have counts for

collaborators

26 papers

math.NT2026

Legendre polynomials and complex multiplication, II: class numbers of quadratic fields and genus 2 supersingular polynomials

Andrew Karl, Patrick Morton

The factorizations over $F_{p}$ of two supersingular polynomials $h_{p} (x)$ and $g_{p} (x)$ for genus $2$ curves, discussed by Ibukiyama, Katsura and Oort in their 1986 paper, ar…

math.AG2025

A quadrilateral half-turn theorem

Igor Minevich, Patrick Morton

If $A B C$ is a given triangle in the plane, $P$ is any point not on the extended sides of $A B C$ or its anticomplementary triangle, $Q$ is the complement of the isotomic conjugate of…

math.NT2023

New proofs of two identities of Ramanujan

Patrick Morton

A proof of several identities of Ramanujan involving theta functions of level $7$ is given which uses a specific modular function for $Γ_{1} (7)$ and Klein's projective representation…

math.NT2022

Periodic points of algebraic functions related to a continued fraction of Ramanujan

Sushmanth J. Akkarapakam, Patrick Morton

A continued fraction $v (τ)$ of Ramanujan is evaluated at certain arguments in the field $K = Q (- d)$ , with $- d \equiv 1$ (mod $8$ ), in which the ideal $(2) = \wp_2 \…

math.NT2022

Explicit congruences for the class equations $H_{- 7 p} (X)$ and $H_{- 28 p} (X)$

Patrick Morton

A computational proof is given for congruences modulo $p$ for the class equation $H_{- 28 p} (X)$ , when the prime $p$ satisfies $p \equiv 3$ (mod $4$ ), and for the product $H_{-7p}(X)…

math.NT2022

The Hasse invariant of the Tate normal form $E_{7}$ and the supersingular polynomial for the Fricke group $Γ_{0}^{*} (7)$

Patrick Morton

A formula is proved for the number of linear factors and irreducible cubic factors over $F_{l}$ of the Hasse invariant $H^_{7, l} (a)$ of the Tate normal form $E_{7} (a)$ for…

Legendre polynomials and complex multiplication, II: class numbers of quadratic fields and genus 2 supersingular polynomials

A quadrilateral half-turn theorem

New proofs of two identities of Ramanujan

Periodic points of algebraic functions related to a continued fraction of Ramanujan

Explicit congruences for the class equations H−7p​(X) and H−28p​(X)

The Hasse invariant of the Tate normal form E7​ and the supersingular polynomial for the Fricke group Γ0∗​(7)

Explicit congruences for the class equations $H_{- 7 p} (X)$ and $H_{- 28 p} (X)$

The Hasse invariant of the Tate normal form $E_{7}$ and the supersingular polynomial for the Fricke group $Γ_{0}^{*} (7)$