A peculiar modular form of weight one
| dc.creator | Kudla, Stephen S. | |
| dc.creator | Rapoport, Michael | |
| dc.creator | Yang, Tonghai | |
| dc.date | 1998-08-31 | |
| dc.date.accessioned | 2026-07-07T05:25:51Z | |
| dc.date.available | 2026-07-07T05:25:51Z | |
| dc.description | In this paper we construct a modular form f of weight one attached to an imaginary quadratic field K. This form, which is non-holomorphic and not a cusp form, has several curious properties. Its negative Fourier coefficients are non-zero precisely for neqative integers -n such that n >0 is a norm from K, and these coefficients involve the exponential integral. The Mellin transform of f has a simple expression in terms of the Dedekind zeta function of K and the difference of the logarithmic derivatives of Riemann zeta function and of the Dirichlet L-series of K. Finally, the positive Fourier coefficients of f are connected with the theory of complex multiplication and arise in the work of Gross and Zagier on singular moduli. | |
| dc.identifier | https://arxiv.org/abs/math/9808143 | |
| dc.identifier | http://arxiv.org/abs/math/9808143 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/77338 | |
| dc.subject | Number Theory | |
| dc.title | A peculiar modular form of weight one | |
| dc.type | text |