A singular modulus is the j-invariant of an elliptic curve with complex multiplication; as such the arithmetic and algebraic properties of these numbers have attracted the interest of mathematicians for centuries. In particular, there are important results concerning the behavior of differences of singular moduli, and also about the multiplicative dependencies that can arise among singular moduli. In joint work with Vahagn Aslanyan and Guy Fowler we show that for every positive integer n there are a finite set S and finitely many algebraic curves T_1,...,T_k with the following property: if (x_1,...,x_n,y) is a tuple of pairwise distinct singular moduli so that the differences (x_1-y),...,(x_n-y) are multiplicatively dependent, then (x_1,..., x_n, y) belongs either to S or to one of the curves T_1,...,T_k.
Multiplicative dependencies among differences of singular moduli
11.03.2025 13:15 - 14:45
Organiser:
H. Grobner, A. Minguez-Espallargas, A. Mellit
Location: