Arithmetic partial differential equations, II: modular curves

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dc.creatorBuium, Alexandru
dc.creatorSimanca, Santiago R.
dc.date2008-04-30
dc.date.accessioned2026-07-07T09:36:04Z
dc.date.available2026-07-07T09:36:04Z
dc.descriptionWe classify ``arithmetic convection equations'' on modular curves, and describe their space of solutions. Certain of these solutions involve the Fourier expansions of the Eisenstein modular forms of weight 4 and 6, while others involve the Serre-Tate expansions of the same modular forms; in this sense, our arithmetic convection equations can be seen as "unifying" the two types of expansions. The theory can be generalized to one of ``arithmetic heat equations'' on modular curves, but we prove that modular curves do not carry ``arithmetic wave equations.'' Finally, we prove an instability result for families of arithmetic heat equations converging to an arithmetic convection equation.
dc.identifierhttps://arxiv.org/abs/0804.4856
dc.identifierhttp://arxiv.org/abs/0804.4856
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/160046
dc.subjectNumber Theory
dc.subjectAnalysis of PDEs
dc.subject11F11; 11F32; 12H05
dc.titleArithmetic partial differential equations, II: modular curves
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