Patrick Morton

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20172021

most citedAffine Maps and Feuerbach'sTheorem

1 citations · 1 across the 4 of their papers we have counts for

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math.NT2021

Supersingular conjectures for the Fricke group

Patrick Morton

A proof is given of several conjectures from a recent paper of Nakaya concerning the supersingular polynomial $s s_{p}^{(N *)} (X)$ for the Fricke group $Γ_{0}^{*} (N)$ , for $N \in \{2, 3, 5…

math.NT2020

Solutions of diophantine equations as periodic points of $p$ -adic algebraic functions, III

Patrick Morton

All the periodic points of a certain algebraic function related to the Rogers-Ramanujan continued fraction $r (τ)$ are determined. They turn out to be $0, \frac{- 1 \pm 5}{2}$ …

math.NT2020

The Hasse invariant of the Tate normal form $E_{5}$ and the class number of $Q (- 5 l)$

Patrick Morton

It is shown that the number of irreducible quartic factors of the form $g (x) = x^{4} + a x^{3} + (11 a + 2) x^{2} - a x + 1$ which divide the Hasse invariant of the Tate normal form $E_{5}$ in character…

math.NT2019

On the Hasse invariants of the Tate normal forms $E_{5}$ and $E_{7}$

Patrick Morton

A formula is proved for the number of linear factors over $F_{l}$ of the Hasse invariant of the Tate normal form $E_{5} (b)$ for a point of order $5$ , as a polynomial in the pa…

math.NT2018

Solutions of diophantine equations as periodic points of $p$ -adic algebraic functions, II: The Rogers-Ramanujan continued fraction

Patrick Morton

In this part we show that the diophantine equation $X^{5} + Y^{5} = ε^{5} (1 - X^{5} Y^{5})$ , where $ε = \frac{- 1 + 5}{2}$ , has solutions in specific abelian extensions of qua…

Supersingular conjectures for the Fricke group

Solutions of diophantine equations as periodic points of p-adic algebraic functions, III

The Hasse invariant of the Tate normal form E5​ and the class number of Q(−5l​)

On the Hasse invariants of the Tate normal forms E5​ and E7​

Solutions of diophantine equations as periodic points of p-adic algebraic functions, II: The Rogers-Ramanujan continued fraction

Solutions of diophantine equations as periodic points of $p$ -adic algebraic functions, III

The Hasse invariant of the Tate normal form $E_{5}$ and the class number of $Q (- 5 l)$

On the Hasse invariants of the Tate normal forms $E_{5}$ and $E_{7}$

Solutions of diophantine equations as periodic points of $p$ -adic algebraic functions, II: The Rogers-Ramanujan continued fraction