New York Journal of Mathematics
Volume 27 (2021), 787-817


Patrick Morton

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

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Published: May 31, 2021.
Keywords: Periodic points, algebraic function, 5-adic field, extended ring class fields, Rogers-Ramanujan continued fraction.
Subject: 11D41,11G07,11G15,14H05.

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



Author information

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