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1 results

D-finite multivariate series with arithmetic restrictions on their coefficients
Part of
Jason Bell, Daniel Smertnig
Journal:

Canadian Journal of Mathematics / Volume 75 / Issue 6 / December 2023

Published online by Cambridge University Press:

03 October 2022, pp. 1745-1779

Print publication:

December 2023
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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.