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Multidimensional small divisor functions

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arxiv 2009.14652 v2 pith:VYQ3PIDV submitted 2020-09-30 math.NT

classification math.NT
keywords arxivdimensionconsiderconstructiondivisorevenexamplesexplicit
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abstract

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 Maa{\ss} 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 $10$.

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