@unpublished{21737,
  abstract     = {In calculus, l'Hopital's rule provides a simple way to evaluate the limits of quotient functions when both the numerator and denominator vanish. But what happens when we move beyond real functions on a real interval? In this article, we study when the quotient of two complex-valued functions in higher dimension can be defined continuously at the points where both functions vanish. Surprisingly, the answer is far subtler than in the real-valued setting. We provide a complete characterization for the continuity of the quotient function. We also point out why extending this result to smoother quotients remains an intriguing challenge.},
  author       = {Chern, Albert and Ishida, Sadashige},
  booktitle    = {arXiv},
  keywords     = {l’Hopital theorem, complex functions},
  title        = {{L'Hopital rules for complex-valued functions in higher dimensions}},
  doi          = {10.48550/ARXIV.2602.09958},
  year         = {2026},
}