On ranks of Jacobian varieties in prime degree extensions
T. Dokchitser [Acta Arith. 126 (2007)] showed that given an elliptic curve E defined over a number field K then there are infinitely many degree 3 extensions L/K for which the rank of E(L) is larger than E(K). In the present paper we show that the same is true if we replace 3 by any prime number. This result follows from a more general result establishing a similar property for the Jacobian varieties associated with curves defined by an equation of the shape f(y) = g(x) where f and g are polynomials...