Geodesic
A residue theorem for rational functions on star-shaped domains
Canadian mathematical bulletin, Tome 68 (2025) no. 3, pp. 908-913

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DOI

M. Heins demonstrated that any finite Blaschke product defined on the open unit disc, provided it has at least one finite pole, possesses a nonzero residue. In this work, we extend Heins’ result by generalizing the class of functions under consideration. Specifically, we prove that a broader class of rational functions, defined on certain star-shaped domains in the complex plane, also exhibits this nonzero residue property. This class includes, as a special case, the family of finite Blaschke products. Our findings contribute to a better understanding of the analytic behavior of rational functions on more complex domains, opening new avenues for exploration in this area.
DOI : 10.4153/S0008439525000165
Mots-clés : Blaschke products, residue, star-shaped domain, level curve 
Nasri, Mostafa. A residue theorem for rational functions on star-shaped domains. Canadian mathematical bulletin, Tome 68 (2025) no. 3, pp. 908-913. doi: 10.4153/S0008439525000165
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     title = {A residue theorem for rational functions on star-shaped domains},
     journal = {Canadian mathematical bulletin},
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     year = {2025},
     volume = {68},
     number = {3},
     doi = {10.4153/S0008439525000165},
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