A Fractional Partial Differential Equation for Theta Functions

Rafael G. Campos ()
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Rafael G. Campos: Universidad de Quintana Roo, División de Ciencias e Ingeniería, Departamento de Ciencias

A chapter in Singularities, Algebraic Geometry, Commutative Algebra, and Related Topics, 2018, pp 579-591 from Springer

Abstract: Abstract We find that theta functions are solutions of a fractional partial differential equation that generalizes the diffusion equation. This equation is the limit of a sequence of differential equations for the partial sums of theta functions where the fractional derivatives are given as differentiation matrices for trigonometric polynomials in their Fourier representation, i.e., given as similarities of diagonal matrices under the ordinary discrete Fourier transform. This fact enables the fast numerical computation of fractional partial derivatives of theta functions and elliptic integrals.

Keywords: 14K25; 33E05; 35R11; 42A15; 65T50 (search for similar items in EconPapers)
Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-96827-8_26

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DOI: 10.1007/978-3-319-96827-8_26

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