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Patrick Morton
Solutions of diophantine equations as periodic points of p-adic algebraic functions, II:
The Rogers-Ramanujan continued fraction
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| Published: |
October 28, 2019. |
| Keywords: |
Periodic points, algebraic functions, 5-adic field, ring class fields,
Rogers-Ramanujan continued fraction. |
| Subject: |
11D41,11G07,11G15,14H05. |
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Abstract
In this part we show that the diophantine equation X5+Y5=ε5(1-X5Y5), where ε=(-1+√5)/2, has solutions in specific abelian extensions of quadratic fields K=Q(√-d) in which -d ≡ ± 1 (mod 5). The coordinates of these solutions are values of the Rogers-Ramanujan continued fraction r(τ), and are shown to be periodic points of an algebraic function. |
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| Acknowledgements
N/A
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| Author information
Patrick Morton:
Department of Mathematical Sciences, LD 270
Indiana University-Purdue University at Indianapolis (IUPUI)
Indianapolis, IN 46202, USA
pmorton@iupui.edu
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