 

Patrick Morton
Solutions of diophantine equations as periodic points of padic algebraic functions, III
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Published: 
May 31, 2021. 
Keywords: 
Periodic points, algebraic function, 5adic field, extended ring class fields, RogersRamanujan continued fraction. 
Subject: 
11D41,11G07,11G15,14H05. 


Abstract
All the periodic points of a certain algebraic function related to the RogersRamanujan continued fraction
r(τ) are explicitly determined. This yields a new class number formula for orders in the fields K_{d}. Conjecture 1 of Part I is proved for the prime p=5, showing that the ring class fields over fields of type K_{d} whose conductors are relatively prime to 5 coincide with the fields generated over Q by the periodic points (excluding 1) of a fixed 5adic algebraic function.


Acknowledgements
N/A


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

