Abstract
We provide a concrete characterization of the poly-analytic planar automorphic functions, a special class of non analytic planar automorphic functions with respect to the Appell–Humbert automorphy factor, arising as images of the holomorphic ones by means of the creation differential operator. This is closely connected to the spectral theory of the magnetic Laplacian on the complex plane.
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Acknowledgements
The authors are grateful to the anonymous referee, his deep and extensive comments greatly contributed to improve this paper. The assistance of the members of both “Ahmed Intissar” and “Analysis, P.D.E. & Spectral Geometry” seminars is gratefully acknowledged.
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Allal, G., Lahcen, I. Complex Creation Operator and Planar Automorphic Functions. Math Phys Anal Geom 26, 28 (2023). https://doi.org/10.1007/s11040-023-09471-8
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DOI: https://doi.org/10.1007/s11040-023-09471-8