The Shimura correspondence relating modular forms of integral and half-integral weight is one of the key theorems in the study of modular forms. One of the insights it enables is the Kohnen-Zagier formula, which relates coefficients of modular forms to central values of L-functions. Recently, Ahlgren, Andersen, and Dicks have proven a Shimura correspondence for eta multipliers. I’ve been using their work to prove a new Kohnen-Zagier formula (from level 1 to level 6). In this talk I will be discussing a key feature of the theory of Kohnen-Zagier formulae, a relation between Kloosterman sums and Quadratic Forms (through Weyl Sums), and how one uses the Weil representation to prove such a relation for eta multipliers.
Talk by Clayton Williams.