1 citations · 1 across the 6 of their papers we have counts for
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Rational points on modular curves: parameterization and geometric explanations
Maarten Derickx, Sachi Hashimoto, Filip Najman +1
We show that, conditional on Zywina's effective version of the Serre uniformity conjecture, there is a natural way to parameterize non-CM -rational points on all modula…
Hecke reciprocity and class groups
Ari Shnidman, Artane Siad
We compute the average size of in the family of cubic fields . Specifically, as varies over the subfamily of wildly (resp. tamel…
Rank stability in quadratic extensions and Hilbert's tenth problem for the ring of integers of a number field
Levent Alpöge, Manjul Bhargava, Wei Ho +1
We show that for any quadratic extension of number fields , there exists an abelian variety of positive rank whose rank does not grow upon base change to . This resul…
A positive proportion of quartic fields are not monogenic yet have no local obstruction to being so
Levent Alpöge, Manjul Bhargava, Ari Shnidman
We show that a positive proportion of quartic fields are not monogenic, despite having no local obstruction to being monogenic. Our proof builds on the corresponding result for cub…
A positive proportion of cubic fields are not monogenic yet have no local obstruction to being so
Levent Alpöge, Manjul Bhargava, Ari Shnidman
We show that a positive proportion of cubic fields are not monogenic, despite having no local obstruction to being monogenic. Our proof involves the comparison of -descent and $…
Quadratic twists of abelian varieties with real multiplication
Ari Shnidman
Let be a totally real number field and a principally polarized abelian variety with real multiplication by the ring of integers of a totally real field. Ass…