Year: 2025
Type: preprint
Abstract: We study Appell functions associated to an arbitrary positive definite lattice $Λ$ and a choice of $M\leq {\rm dim}(Λ)$ linearly independent vectors $d_r\in Λ$, $r=1,\dots,M$. These functions are instances of multi-variable quasi-elliptic functions, and specific examples have appeared at various places in mathematics and theoretical physics. For example, if $Λ$ is chosen to be one-dimensional, these functions reduce to the classical Appell function, which is a prominent example in the theory of mock modular forms. The Appell functions introduced here are examples of depth $M$ mock modular forms. We derive a structural formula for their modular completion. Motivated by partition functions in theoretical physics, we discuss the case where $Λ$ is the $A_N$ root lattice in detail.
Source: arXiv (Cornell University)
Authors: Chattopadhyaya, Aradhita, Manschot, Jan
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7091187260
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