Multidimensional Small Divisor Functions

This is a short note generalizing the construction from arXiv:1906.07410, arXiv:2009.04955 to multi-indices. We recommend to consider both references first. We obtain polar harmonic Maaß forms of non-positive integral weight if the dimension is even and greater than $2$. We provide explicit examples in dimension $4$, $6$, $8$, and $10$.

10 pages, no figures, comments welcome

Related Organizations

University of Cologne
Germany
Universtity of Cologne
Germany

Keywords

polar harmonic Maaß forms, Mathematics - Number Theory, FOS: Mathematics, Number Theory (math.NT), Forms of half-integer weight; nonholomorphic modular forms

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