On the transcendence degree of the differential field generated by Siegel modular forms

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dc.creatorBertrand, Daniel
dc.creatorZudilin, Wadim
dc.date2000-06-23
dc.date.accessioned2026-07-07T12:45:56Z
dc.date.available2026-07-07T12:45:56Z
dc.descriptionIt is a classical fact that the elliptic modular functions satisfies an algebraic differential equation of order 3, and none of lower order. We show how this generalizes to Siegel modular functions of arbitrary degree. The key idea is that the partial differential equations they satisfy are governed by Gauss--Manin connections, whose monodromy groups are well-known. Modular theta functions provide a concrete interpretation of our result, and we study their differential properties in detail in the case of degree 2.
dc.description21 pages, AmSTeX, uses picture.sty for 1 LaTeX picture; submitted for publication
dc.identifierhttps://arxiv.org/abs/math/0006176
dc.identifierhttp://arxiv.org/abs/math/0006176
dc.identifierJ. Reine Angew. Math. 554 (January 2003), 47--68
dc.identifierdoi:10.1515/crll.2003.008
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/221216
dc.subjectNumber Theory
dc.subjectAlgebraic Geometry
dc.subject11J89, 11F46 (Primary), 11F27, 14G35 (Secondary)
dc.titleOn the transcendence degree of the differential field generated by Siegel modular forms
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