### The Macdonald identities and Jacobi forms of lattice index

Heilbronn Number Theory Seminar

31st October 2018, 4:00 pm – 5:00 pm

Howard House, 4th Floor Seminar Room

We propose a new and short proof for the Macdonald identities using only some easy facts from the theory of Jacobi forms of lattice index and classical root systems. (The needed basic features of these theories will be explained in the talk). We discuss applications and open questions related to the new proof, and we end the talk by deducing from the Macdonald identities, for 42 elliptic curves over the rationals and of rank 1 product identities for the (classical) Jacobi forms attached to elliptic curves by the theory of modular forms.

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