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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…
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…