New York Journal of Mathematics
Volume 25 (2019), 1178-1213


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.

In this part we show that the diophantine equation X5+Y55(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.



Author information

Patrick Morton:
Department of Mathematical Sciences, LD 270
Indiana University-Purdue University at Indianapolis (IUPUI)
Indianapolis, IN 46202, USA