Abstract for the seminar talk on 04.04.2008

Dr. Cormac O'Sullivan (Bronx Community College of the CUNY)
Higher-order cusp forms, inner products and Kronecker limits
Time: 14.15 / Place: HWZ (HG G43)

Higher-order cusp forms arose in work of Eichler, Goldfeld and Zagier in three different contexts. They generalize classical cuspforms and are also a special case of the vector-valued cusp forms of Knopp and Mason. In joint work with Imamoglu, we show that the second-order space has a natural inner product. We conjecture that this method also gives inner products for all higher-order spaces. This work relies on properties of non-holomorphic higher-order Eisenstein series. Working with Jorgenson, we identify the Kronecker limits for these series and find new analogs of the Dedekind sum.