Vol. 13, No. 4, 2019

Download this article
Download this article For screen
For printing
Recent Issues

Volume 13
Issue 7, 1509–1763
Issue 6, 1243–1507
Issue 5, 995–1242
Issue 4, 749–993
Issue 3, 531–747
Issue 2, 251–530
Issue 1, 1–249

Volume 12, 10 issues

Volume 11, 10 issues

Volume 10, 10 issues

Volume 9, 10 issues

Volume 8, 10 issues

Volume 7, 10 issues

Volume 6, 8 issues

Volume 5, 8 issues

Volume 4, 8 issues

Volume 3, 8 issues

Volume 2, 8 issues

Volume 1, 4 issues

The Journal
About the Journal
Subscriptions
Editorial Board
Editors' Interests
Submission Guidelines
Submission Form
Editorial Login
Ethics Statement
Author Index
To Appear
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Other MSP Journals
This article is available for purchase or by subscription. See below.
Cycle integrals of modular functions, Markov geodesics and a conjecture of Kaneko

Paloma Bengoechea and Özlem Imamoglu

Vol. 13 (2019), No. 4, 943–962
Abstract

In this paper we study the values of modular functions at the Markov quadratics which are defined in terms of their cycle integrals along the associated closed geodesics. These numbers are shown to satisfy two properties that were conjectured by Kaneko. More precisely we show that the values of a modular function f, along any branch B of the Markov tree, converge to the value of f at the Markov number which is the predecessor of the tip of B. We also prove an interlacing property for these values.

PDF Access Denied

However, your active subscription may be available on Project Euclid at
https://projecteuclid.org/ant

We have not been able to recognize your IP address 34.204.176.189 as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recom­mendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 40.00:

Keywords
modular forms, cycle integrals, markov numbers, j-invariant
Mathematical Subject Classification 2010
Primary: 11F03
Secondary: 11J06
Milestones
Received: 27 March 2018
Revised: 18 December 2018
Accepted: 8 February 2019
Published: 6 May 2019
Authors
Paloma Bengoechea
Department of Mathematics
ETH Zurich
Switzerland
Özlem Imamoglu
Department of Mathematics
ETH Zurich
Switzerland