Integral representations for solutions of exponential Gauss-Manin systems

2007/04/13 by Marco Hien, Hien, Marco, Céline Roucairol +1
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Nonlinear Waves and Solitons #Algebraic Geometry and Number Theory

paper · doi:10.48550/arxiv.0704.1739

Abstract

Let f,g be two algebraically independent regular functions from the smooth affine complex variety U to the affine line. The associated exponential Gauss-Manin systems on the affine line are defined to be the cohomology sheaves of the direct image of the exponential differential system O_U e^g with respect to f. We prove that its holomorphic solutions admit representations in terms of period integrals over topological chains with possibly closed support and with rapid decay condition.

Citations

• Stratifications de Whitney et théorème de Bertini-Sard

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