Geodesic
D-finite multivariate series with arithmetic restrictions on their coefficients
Canadian journal of mathematics, Tome 75 (2023) no. 6, pp. 1745-1779

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DOI

A multivariate, formal power series over a field K is a Bézivin series if all of its coefficients can be expressed as a sum of at most r elements from a finitely generated subgroup $G \le K^*$; it is a Pólya series if one can take $r=1$. We give explicit structural descriptions of D-finite Bézivin series and D-finite Pólya series over fields of characteristic $0$, thus extending classical results of Pólya and Bézivin to the multivariate setting.
DOI : 10.4153/S0008414X22000517
Mots-clés : D-finite series, Pólya series, S-unit equations, finitely generated groups 
Bell, Jason; Smertnig, Daniel. D-finite multivariate series with arithmetic restrictions on their coefficients. Canadian journal of mathematics, Tome 75 (2023) no. 6, pp. 1745-1779. doi: 10.4153/S0008414X22000517
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     title = {D-finite multivariate series with arithmetic restrictions on their coefficients},
     journal = {Canadian journal of mathematics},
     pages = {1745--1779},
     year = {2023},
     volume = {75},
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     doi = {10.4153/S0008414X22000517},
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