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Values of modular functions at real quadratics and conjectures of Kaneko

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In 2008, Kaneko made several interesting observations about the values of the modular j invariant at real quadratic irrationalities. The values of modular functions at real quadratics are defined in… Click to show full abstract

In 2008, Kaneko made several interesting observations about the values of the modular j invariant at real quadratic irrationalities. The values of modular functions at real quadratics are defined in terms of their cycle integrals along the associated geodesics. In this paper we prove some of the conjectures of Kaneko for a general modular function.

Keywords: values modular; modular functions; real quadratics; conjectures kaneko; quadratics conjectures; functions real

Journal Title: Mathematische Annalen
Year Published: 2018

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