Polynomial vector fields in ℂ^∞ determining differentiation of hyperelliptic functions of any genus

2025/12/16 by Bunkova, E. Yu.
#Commutative Algebra (math.AC) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences

paper · doi:10.48550/arxiv.2512.14605

Abstract

In this work we give direct proofs of two theorems concerning explicitly defined polynomial vector fields connected to differentiation of hyperelliptic functions of any genus. We prove that the operators determining the fields commute, and we show that each of them annul polynomials defined in terms of generating functions in ℂ^∞.

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