 

Patrick Morton
Solutions of diophantine equations as periodic points of padic algebraic functions, II:
The RogersRamanujan continued fraction
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Published: 
October 28, 2019. 
Keywords: 
Periodic points, algebraic functions, 5adic field, ring class fields,
RogersRamanujan continued fraction. 
Subject: 
11D41,11G07,11G15,14H05. 


Abstract
In this part we show that the diophantine equation X^{5}+Y^{5}=ε^{5}(1X^{5}Y^{5}), 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 RogersRamanujan continued fraction r(τ), and are shown to be periodic points of an algebraic function. 

Acknowledgements
N/A


Author information
Patrick Morton:
Department of Mathematical Sciences, LD 270
Indiana UniversityPurdue University at Indianapolis (IUPUI)
Indianapolis, IN 46202, USA
pmorton@iupui.edu

