Early work of H. Cohn and N. Elkies on the sphere-packing problem in dimension 8 described the lacking ingredients as ``magic functions'' due to the unusual transformation properties required to satisfy the constraints of the problem. It was M. Viazovska's identification of the ``magic functions'' as quasiautomorphic forms that led to solutions in both 8 and 24 dimensions. Quasiautomorphic forms generalize automorphic forms, but their transformation behavior is more complicated than that of automorphic forms -- perhaps what caused them to be neglected for so long. The Hecke vector-forms is a language for quasiautomorphic forms that preserves the automorphic transformational symmetry.
Hecke vector-forms
27.05.2025 13:15 - 14:45
Organiser:
H. Grobner, A. Minguez-Espallargas, A. Mellit
Location: