A peculiar modular form of weight one

dc.creatorKudla, Stephen S.
dc.creatorRapoport, Michael
dc.creatorYang, Tonghai
dc.date1998-08-31
dc.date.accessioned2026-07-07T05:25:51Z
dc.date.available2026-07-07T05:25:51Z
dc.descriptionIn 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.identifierhttps://arxiv.org/abs/math/9808143
dc.identifierhttp://arxiv.org/abs/math/9808143
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/77338
dc.subjectNumber Theory
dc.titleA peculiar modular form of weight one
dc.typetext

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