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Galois Seminar

Friday, October 14, 2022 - 3:15pm

Souparna Purohit

University of Pennsylvania


University of Pennsylvania

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The successive minima of a lattice L in a Euclidean space V is an important set of invariants. For instance, there are post-quantum cryptosystems based on the difficulty of finding the shortest non-zero vector in a lattice, the length of which is equal to the first successive minima. We are interested in studying the successive minima of the sequence of pairs (L_k, V_k), where L_k denotes the lattice of integral modular forms of weight 12k for a fixed level N, and V_k denotes its real span, made into a Euclidean space with respect to the norm induced by the Petersson inner product. We prove that as k goes off to infinity, the sequence of these successive minima, scaled and weighted appropriately, converges in a distributional sense. We also make some remarks about how these limiting distributions compare as we vary the levels.