2023/03/06 by Eszter Gselmann, Gselmann, Eszter, Gergely Kiss +1
Computer Science · Mathematics · #13N15 #16W20 #39B32 #39B72 #43A45 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry and Number Theory #Classical Analysis and ODEs (math.CA) #Coding theory and cryptography #Commutative Algebra (math.AC) #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2303.03306
openalex publication_date 2023/03/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this sequence of work we investigate polynomial equations of additive functions. We consider the solutions of equation ∑i=1nfi(x^pi)gi(x)^qi= 0 (x∈ \mathbbF), where n is a positive integer, \mathbbF⊂ ℂ is a field, fi, gi\colon \mathbbF→ ℂ are additive functions and pi, qi are positive integers for all i=1, …, n. Using the theory of decomposable functions we describe the solutions as compositions of higher order derivations and field homomorphisms. In many cases we also give a tight upper bound for the order of the involved derivations. Moreover, we present the full description of the solutions in some important special cases, too.