Abstract
We prove a new transference theorem in the geometry of numbers, giving optimal bounds relating the successive minima of a lattice with the minimal length of generating vectors of its dual. It generalizes the transference theorem due to Banaszczyk. The theorem is motivated by our efforts to improve Ajtai's connection factors in the connection of average-case to worst-case complexity of the shortest lattice vector problem. Our proofs are non-constructive, based on methods from harmonic analysis.
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