3 papers
math.AG2026
Counterexamples to the Jacobian conjecture in dimensions greater than two
Shuhong Gao
The Jacobian conjecture, open since 1939, asks whether every polynomial map of $\C^n$ whose Jacobian determinant is a nonzero constant must have a polynomial inverse. It was refute…
cs.CC2025
Bounded Distance Decoding for Random Lattices
Shuhong Gao
The current paper investigates the bounded distance decoding (BDD) problem for ensembles of lattices whose generator matrices have sub-Gaussian entries. We first prove that, for th…
math.NT2024
On binomial Weil sums and an application
Kaimin Cheng, Shuhong Gao
Let be a prime, and be a positive integer not divisible by . Denote by the multiplicative order of modulo . Let represent the fini…