Mark Chambers

Modular forms of half-integral weight, and twisted L-Values

Theta lifting between O(2,1) and Mp(2) realises the classical correspondence of weight 2k and weight k+1/2 modular forms due to Shimura, Shintani, etc. In this setting, Kohnen-Zagier gave the first explicit formula for Fourier coefficients in terms of twisted L-Values, though this was under the so-called “Heegner hypothesis” on quadratic residues. Inspired by Baruch-Mao, we use a construction of Kojima-Tokuno to produce half-integral weight forms that give the other twisted L-values.