 

Sushmanth J. Akkarapakam and
Patrick Morton
Periodic points of algebraic functions related to a continued fraction of Ramanujan
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print


Published: 
June 3, 2024. 
Keywords: 
Periodic points, algebraic function, 2adic field, extended ring class fields, Ramanujan continued fraction. 
Subject [2020]: 
14H05, 37F05, 11R37, 11D88, 11R29. 


Abstract
A continued fraction v(τ) of Ramanujan is evaluated at certain arguments in the field K = Q(\sqrt{d}), with d = 1 (mod 8), in which the ideal (2) =
P_{2} P'_{2} is a product of two prime ideals. These values of v(τ) are shown to generate the inertia field of P_{2} or P'_{2} in an extended ring class field over the field K. The conjugates over Q of these same values, together with 0, 1 ± \sqrt{2}, are shown to form the exact set of periodic points of a fixed algebraic function F(x), independent of d. These are analogues of similar results for the RogersRamanujan continued fraction.


Acknowledgements
N/A


Author information
Sushmanth J. Akkarapakam
Department of Mathematics
University of Missouri at Columbia
208 Math Sci Building, 810 Rollins St.
Columbia, MO 65211, USA
akkarapakams@missouri.edu
Patrick Morton
Department of Mathematical Sciences
Indiana UniversityPurdue University at Indianapolis (IUPUI)
402 N. Blackford St., LD 270
Indianapolis, IN 46202, USA
pmorton@iu.edu

