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 ...

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 ...

Modular Forms and Special Cycles on Shimura Curves is a thorough study of the generating functions constructed from special cycles, both divisors and zero-cycles, on the arithmetic surface "M" ...

We all know the usual jokes about the ‘S’ in ‘IoT’ standing for ‘Security’. It’s hardly a secret that security in embedded, networked devices (‘IoT devices’) is all too often a last-minute task that ...

Quantum modular forms have emerged as a versatile framework that bridges classical analytic number theory with quantum topology and mathematical physics. Initially inspired by the pioneering work on ...

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 ...

Manjul Bhargava was warned long ago never to think about math while driving. "I find doing mathematical research requires very deep concentration," said Bhargava, the Brandon Fradd, Class of 1983, ...

“Elliptic curve cryptography (ECC), as one of the public key cryptography systems, has been widely applied to many security applications. It is challenging to implement a scalar multiplication (SM) ...

A bounty of $12,288 has been announced for the first person to crack the NIST elliptic curves seeds and discover the original phrases that were hashed to generate them. The bounty will be tripled to ...