Instytut Matematyczny Polskiej Akademii Nauk / pl / Wydawnictwa / Czasopisma IMPAN / Acta Arithmetica / Artykuły Online First

Streszczenie

Since the 2022 work of Huber and Wüstholz one knows practically all there is to know about the transcendence and linear independence of path integrals of algebraic functions in a single variable. Here we focus on elliptic integrals and give simple necessary and sufficient conditions for the transcendence. Our conditions use the classical concept of elementary differential and are particularly suitable as an effective decision procedure, even for families of integrals. We supply some lemniscatic examples, also for genus 0 and 2.