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2019 Cycle integrals of modular functions, Markov geodesics and a conjecture of Kaneko
Paloma Bengoechea, Özlem Imamoglu
Algebra Number Theory 13(4): 943-962 (2019). DOI: 10.2140/ant.2019.13.943

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.

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Paloma Bengoechea. Özlem Imamoglu. "Cycle integrals of modular functions, Markov geodesics and a conjecture of Kaneko." Algebra Number Theory 13 (4) 943 - 962, 2019. https://doi.org/10.2140/ant.2019.13.943

Information

Received: 27 March 2018; Revised: 18 December 2018; Accepted: 8 February 2019; Published: 2019
First available in Project Euclid: 18 May 2019

zbMATH: 07059760
MathSciNet: MR3951584
Digital Object Identifier: 10.2140/ant.2019.13.943

Subjects:
Primary: 11F03
Secondary: 11J06

Rights: Copyright © 2019 Mathematical Sciences Publishers

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Vol.13 • No. 4 • 2019
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