57 citations · 75 across the 5 of their papers we have counts for
6 papers
Fourier coefficients of sextic theta series
Reinier Broker, Jeff Hoffstein
This article focuses on the theta series on the 6-fold cover of GL. We investigate the Fourier coefficients of the theta series, and give partially proven, partially con…
Evaluating Igusa functions
Reinier Broker, Kristin Lauter
The moduli space of principally polarized abelian surfaces is parametrized by three Igusa functions. In this article we investigate a new way to evaluate these functions by using S…
Modular polynomials via isogeny volcanoes
Reinier Broker, Kristin Lauter, Andrew V. Sutherland
We present a new algorithm to compute the classical modular polynomial Phi_n in the rings Z[X,Y] and (Z/mZ)[X,Y], for a prime n and any positive integer m. Our approach uses the gr…
An explicit height bound for the classical modular polynomial
Reinier Broker, Andrew V. Sutherland
For a prime m, let Phi_m be the classical modular polynomial, and let h(Phi_m) denote its logarithmic height. By specializing a theorem of Cohen, we prove that h(Phi_m) <= 6 m log…
Modular polynomials for genus 2
Reinier Broker, Kristin Lauter
Modular polynomials are an important tool in many algorithms involving elliptic curves. In this article we investigate their generalization to the genus 2 case following pioneering…
Computing Hilbert Class Polynomials
Juliana Belding, Reinier Bröker, Andreas Enge +1
We present and analyze two algorithms for computing the Hilbert class polynomial . The first is a p-adic lifting algorithm for inert primes p in the order of discriminant D <…