Dimensional interpolation and the Selberg integral

Golyshev, V.; van Straten, D.; Zagier, D.

doi:10.1016/j.geomphys.2019.06.006

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Dimensional interpolation and the Selberg integral

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Zagier, D.
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.1016/j.geomphys.2019.06.006
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arXiv:1906.00071.pdf
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Golyshev, V., van Straten, D., & Zagier, D. (2019). Dimensional interpolation and the Selberg integral. Journal of Geometry and Physics, 145: 103455. doi:10.1016/j.geomphys.2019.06.006.

Cite as: https://hdl.handle.net/21.11116/0000-0004-9D01-A

Abstract

We show that a version of dimensional interpolation for the Riemann–Roch–Hirzebruch formalism in the case of a Grassmannian leads to an expression for the Euler characteristic of line bundles in terms of a Selberg integral. We propose a way to interpolate higher Bessel equations, their wedge powers, and monodromies thereof to non-integer orders, and link the result with the dimensional interpolation of the RRH formalism in the spirit of the gamma conjectures.