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math.NT2018
Values of modular functions at real quadratics and conjectures of Kaneko
Paloma Bengoechea, Ozlem Imamoglu
In 2008, M. Kaneko made several interesting observations about the values of the modular j invariant at real quadratic irrationalities. The values of modular functions at real quad…
math.NT2018
Metric number theory of Fourier coefficients of modular forms
Paloma Bengoechea
We discuss the approximation of real numbers by Fourier coefficients of newforms, following recent work of Alkan, Ford and Zaharescu. The main tools used here, besides the (now pro…
math.NT2018
Cycle integrals of modular functions, Markov geodesics and a conjecture of Kaneko
Paloma Bengoechea, Ozlem Imamoglu
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 num…