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July 15, 2026Research in the Mathematical SciencesOpen Access

Appell functions for general lattices

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Authors

ACAradhita ChattopadhyayaJMJan Manschot

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Overview

Derives structural formulas for Appell functions in general lattices, highlighting their relevance in theoretical physics.

Key Points

  • This research focuses on developing Appell functions linked to positive definite lattices and exploring their mathematical significance.
  • Analyzed Appell functions for an arbitrary positive definite lattice with M independent vectors.
  • Derived structural formulas for modular completion of these functions.
  • Special attention was given to the A_N root lattice and its application in theoretical physics.
  • Demonstrated that Appell functions for one-dimensional lattices reduce to classical Appell functions in mock modular forms.
  • Established explicit structural formulas that delineate the modular properties of the new Appell functions.
  • Discussed connections between these functions and partition functions in theoretical physics.

Cite This Study

Chattopadhyaya et al. (2026) studied this question.

synapsesocial.com/papers/6a5722be88b21df87547faf8https://doi.org/10.1007/s40687-026-00643-w
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