2 citations · 3 across the 3 of their papers we have counts for
6 papers
Asymptotic bounds for cycle integrals of the j-function on Markov geodesics
Paloma Bengoechea
We give asymptotic upper and lower bounds for the real and imaginary parts of cycle integrals of the classical modular j-function along geodesics that correspond to Markov irration…
Thue inequalities with few coefficients
Paloma Bengoechea
Let be a binary form with integer coefficients, degree and irreducible over the rationals. Suppose that only of the coefficients of are nonz…
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…
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…
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…
From continued fractions and quadratic functions to modular forms
Paloma Bengoechea
In this paper we study certain real functions defined in a very simple way by Zagier as sums of infinite powers of quadratic polynomials with integer coefficients. These functions…