10 citations · 20 across the 8 of their papers we have counts for
8 papers
A robust implementation for solving the -unit equation and several applications
Alejandra Alvarado, Angelos Koutsianas, Beth Malmskog +3
Let be a number field, and a finite set of places in containing all infinite places. We present an implementation for solving the -unit equation , $x,y \i…
Cyclic covers and Ihara's Question
Christopher Rasmussen, Akio Tamagawa
Let be a rational prime and a number field. Given a superelliptic curve of -power degree, we describe the field generated by the -power torsion of the…
Abelian surfaces good away from 2
Christopher Rasmussen, Akio Tamagawa
Fix a number field and a rational prime . We consider abelian varieties whose -power torsion generates a pro- extension of which is unram…
Picard curves over Q with good reduction away from 3
Beth Malmskog, Christopher Rasmussen
Inspired by methods of N. P. Smart, we describe an algorithm to determine all Picard curves over Q with good reduction away from 3, up to Q-isomorphism. A correspondence between th…
Arithmetic of abelian varieties with constrained torsion
Christopher Rasmussen, Akio Tamagawa
Let be a number field. We present several new finiteness results for isomorphism classes of abelian varieties over whose -power torsion fields are arithmetically cons…
Character sums determined by low degree isogenies of elliptic curves
Dustin Moody, Christopher Rasmussen
We consider character sums determined by isogenies of elliptic curves over finite fields. We prove a congruence condition for character sums attached to arbitrary cyclic isogenies,…