2 citations · 2 across the 10 of their papers we have counts for
11 papers
A cyclotomic gluing construction for lattice sphere packings
Nihar Gargava, Matthias Gröbner, Michael Simkin
For a positive integer , let denote the supremum of the densities of lattice sphere packings in . We prove that, for every sufficiently large , $Δ_d^L \g…
On two counterexamples in the geometry of numbers
Nihar Gargava
We give counterexamples to two optimization problems in dimensions eight and nine. 1. The Cartesian-product problem posed by Cassels for critical determinants and later formulated…
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…
Buildings for Synthesis with Clifford+R
Mark Deaconu, Nihar Gargava, Amolak Ratan Kalra +2
We study the problem of exact synthesis for the Clifford+R gate set and give the explicit structure of the underlying Bruhat-Tits building for this group. In this process, we also…
Density of shapes of periodic tori in the cubic case
Nguyen-Thi Dang, Nihar Gargava, Jialun Li
Consider the compact orbits of the action of the diagonal group on , the so-called periodic tori. Fo…
Mean Value for Random Ideal Lattices
Nihar Gargava, Maryna Viazovska
We investigate the average number of lattice points within a ball for the th cyclotomic number field, where the lattice is chosen at random from the set of unit determinant idea…
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 $…
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…
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.…