Showing math.NTShow all
3 papers · 1 filter
math.NT2025
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.…
math.NT2025
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…
math.NT2021
Lattice packings through division algebras
Nihar Prakash Gargava
In this article, we will show the existence of lattice packings in a sparse family of dimensions. This construction will be a generalisation of Venkatesh's lattice packing result.…