Let f be a newform, as specified by its Hecke eigenvalues, on a Shimura curve X. We describe a method for evaluating f. The most interesting case is when X arises as a compact quotient of the ...

Mathematicians from 12 countries – including one with Maltese heritage - have launched a massive database of mathematical objects including elliptic curves, and a special class of zeroes, that has ...

An international group of mathematicians at MIT and other institutions has released a new online resource that provides detailed maps of previously uncharted mathematical terrain. The "L-functions and ...

In this paper we determine the quadratic points on the modular curves 𝑋₀(𝑁), where the curve is non-hyperelliptic, the genus is 3, 4, or 5, and the Mordell–Weil group of 𝐽₀(𝑁) is finite. The ...

Author Nick Sullivan worked for six years at Apple on many of its most important cryptography efforts before recently joining CloudFlare, where he is a systems engineer. He has a degree in mathematics ...

In August, a pair of mathematicians discovered an exotic, record-breaking curve. In doing so, they tapped into a major open question about one of the oldest and most fundamental kinds of equations in ...

Using “refreshingly old” tools, mathematicians resolved a 50-year-old conjecture about how to categorize important functions called modular forms, with consequences for number theory and theoretical ...