2 citations · 4 across the 9 of their papers we have counts for
11 papers
Module lattices and their shortest vectors
Nihar Gargava, Vlad Serban, Maryna Viazovska +1
We study the shortest vector lengths in module lattices over arbitrary number fields, with an emphasis on cyclotomic fields. In particular, we sharpen the techniques of arXiv:2308.…
Integral Matrices of Fixed Rank over Number Fields
Nihar Gargava, Vlad Serban, Maryna Viazovska +1
We prove an asymptotic formula for the number of fixed rank matrices with integer coefficients over a number field K/Q and bounded norm. As an application, we derive an approximate…
Effective module lattices and their shortest vectors
Nihar Gargava, Vlad Serban, Maryna Viazovska +1
We prove tight probabilistic bounds for the shortest vectors in module lattices over number fields using the results of arXiv:2308.15275. Moreover, establishing asymptotic formulae…
Moments of the number of points in a bounded set for number field lattices
Nihar Gargava, Vlad Serban, Maryna Viazovska
We examine the moments of the number of lattice points in a fixed ball of volume for lattices in Euclidean space which are modules over the ring of integers of a number field $…
Non-vanishing of critical -values in Hida families
Robert Pollack, Vlad Serban
We study the vanishing of as runs through all classical forms in a -adic Hida family (including forms with arbitrarily high nebentype at ), runs through al…
Dense packings via lifts of codes to division rings
Nihar Gargava, Vlad Serban
We obtain algorithmically effective versions of the dense lattice sphere packings constructed from orders in -division rings by the first author. The lattices in questi…
Unlikely intersections on the -adic formal ball
Vlad Serban
We investigate generalizations along the lines of the Mordell--Lang conjecture of the author's -adic formal Manin--Mumford results for -dimensional -divisible formal group…
On -adic versions of the Manin-Mumford Conjecture
Vlad Serban
We prove -adic versions of a classical result in arithmetic geometry stating that an irreducible subvariety of an abelian variety with dense torsion has to be the translate of a…
The Lang-Trotter Conjecture for products of non-CM elliptic curves
Hao Chen, Nathan Jones, Vlad Serban
Inspired by the work of Lang-Trotter on the densities of primes with fixed Frobenius traces for elliptic curves defined over and by the subsequent generalization of Co…
A finiteness result for -adic families of Bianchi modular forms
Vlad Serban
We study -adic families of cohomological automorphic forms for over imaginary quadratic fields and prove that families interpolating a Zariski-dense set of cl…
An Infinitesimal -adic Multiplicative Manin-Mumford Conjecture
Vlad Serban
Our results concern analytic functions on the open unit -adic poly-disc in centered at the multiplicative unit and we prove that such functions only vanish at f…