We calculate explicitly the j-invariants of the elliptic curves corresponding to rational points on the modular curve X+ ns(11) by giving an expression defined over Q of the j-function in terms ofâ€¦ (More)

Another derivation of an explicit parametrisation of Siegelâ€™s modular curve of level 5 is obtained with applications to the class number one problem.

Let n â‰¥ 3. This paper is concerned with the equation a3 + b3 = cn, which we attack using a combination of the modular approach (via Frey curves and Galois representations) with obstructions to theâ€¦ (More)

The aim of this text is to give another proof of a recent result of Imin Chen, concerning certain identities among zeta functions of modular curves, or, equivalently, isogenies between products ofâ€¦ (More)

A number is normal to the base r if, in its expansion to that base, all possible digit strings of length t are equally frequent for each t. While it is generally believed that many familiarâ€¦ (More)

We confirm a conjecture of Merel describing a certain relation between the jacobians of various quotients of X(p) in terms of specific correspondences.

Given a prime p and cusp forms f1 and f2 on some Î“1(N) that are eigenforms outside Np and have coefficients in the ring of integers of some number field K, we consider the problem of deciding whetherâ€¦ (More)

This paper shows that a certain type of Soto-Andrade sum can be estimated in an elementary way which does not use the Riemann hypothesis for curves over finite fields and which slightly sharpensâ€¦ (More)