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On the divergence of the Rogers--Ramanujan continued fraction on the Salem points

Hindov, Raul LU (2019) In Master's Theses in Mathematical Sciences MATM01 20182
Mathematics (Faculty of Engineering)
Mathematics (Faculty of Sciences)
Abstract
The Rogers-Ramanujan continued fraction converges inside the unit circle and diverges outside of it. Its behavior on the unit circle is subtle, there is a countable dense set where it converges, a countable dense set where it diverges, and for the remaining uncountable set the question of convergence is mostly unsolved. The Bowman-McLaughlin conjecture says that we have divergence almost everywhere on the unit circle. We show some evidence for the divergence on a Salem point.
Popular Abstract (Swedish)
På divergensen av Rogers-Ramanujans kedjebråk i Salem punkter.

Rogers-Ramanujans kedjebråk konvergerar inuti enhetscirkeln och divergerar utanför den. Dess beteende på enhetscirkeln är subtil, det finns en uppräknelig tät mängd där det konvergerar, en uppräknelig tät mängd där det divergerar, och för den återstående överuppräkneliga mängden är frågan om konvergens mestadels olöst. Bowman-McLaughlin-förmodan säger att vi har divergens nästan överallt på enhetscirkeln. Vi visar några bevis för divergensen på en Salem-punkt.
Please use this url to cite or link to this publication:
author
Hindov, Raul LU
supervisor
organization
course
MATM01 20182
year
type
H2 - Master's Degree (Two Years)
subject
keywords
Continued fractions, Rogers-Ramanujan, Salem numbers
publication/series
Master's Theses in Mathematical Sciences
report number
LUNFMA-3102-2019
ISSN
1404-6342
other publication id
2019:E11
language
English
id
8973182
date added to LUP
2024-09-30 14:39:43
date last changed
2024-09-30 14:39:43
@misc{8973182,
  abstract     = {{The Rogers-Ramanujan continued fraction converges inside the unit circle and diverges outside of it. Its behavior on the unit circle is subtle, there is a countable dense set where it converges, a countable dense set where it diverges, and for the remaining uncountable set the question of convergence is mostly unsolved. The Bowman-McLaughlin conjecture says that we have divergence almost everywhere on the unit circle. We show some evidence for the divergence on a Salem point.}},
  author       = {{Hindov, Raul}},
  issn         = {{1404-6342}},
  language     = {{eng}},
  note         = {{Student Paper}},
  series       = {{Master's Theses in Mathematical Sciences}},
  title        = {{On the divergence of the Rogers--Ramanujan continued fraction on the Salem points}},
  year         = {{2019}},
}