3 citations · 10 across the 12 of their papers we have counts for
15 papers
Thue equations that simultaneously fail the Hasse principle
Paloma Bengoechea
We refine a previous construction by Akhtari and Bhargava so that, for every positive integer m, we obtain a positive proportion of Thue equations F(x; y) = h that fail the integra…
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…
Representation of integers by sparse binary forms
Shabnam Akhtari, Paloma Bengoechea
We will give new upper bounds for the number of solutions to the inequalities of the shape , where is a sparse binary form, with integer coefficients,…
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…
Irreducibility and Galois group of Hecke polynomials
Paloma Bengoechea
Let T_{n,k}(X) be the characteristic polynomial of the n-th Hecke operator acting on the space of cusp forms of weight k for the full modular group. We show that if there exists n>…
A note on badly approximable linear forms on manifolds
Paloma Bengoechea, Nikolay Moshchevitin, Natalia Stepanova
This paper is motivated by Davenport's problem and the subsequent work regarding badly approximable points in submanifolds of a Euclidian space. We study the problem in the area of…
Badly approximable points in twisted Diophantine approximation and Hausdorff dimension
Paloma Bengoechea, Nikolay Moshchevitin
For any j_1,...,j_n>0 with j_1+...+j_n=1 and any x \in R^n, we consider the set of points y \in R^n for which max_{1\leq i\leq n}(||qx_i-y_i||^{1/j_i})>c/q for some positive consta…
Galois action on special theta values
Paloma Bengoechea
Using Shimura's reciprocity law, we calculate the Galois action on the special values of theta functions associated to primitive Dirichlet characters of odd conductor, normalised b…
On the Mixed Littlewood Conjecture and continued fractions in quadratic fields
Paloma Bengoechea, Evgeniy Zorin
We show how a recent result by Aka and Shapira on the evolution of continued fractions in a fixed quadratic field implies the classic result of de Mathan and Teullié on the Mixed L…
Meromorphic analogues of modular forms generating the kernel of Shintani's lift
Paloma Bengoechea
We study the meromorphic modular forms defined as sums of -k (k>1) powers of integral quadratic polynomials with negative discriminant. These functions can be viewed as meromorphic…
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…
On a theorem of Serret on continued fractions
Paloma Bengoechea
A classical theorem in continued fractions due to Serret shows that for any two irrational numbers x and y related by a transformation in PGL(2,Z) there exist s and t for which…