Year: 2019
Type: preprint
Abstract: We define transalgebraic functions on a compact Riemann surface as meromorphic functions except at a finite number of punctures where they have finite order exponential singularities. This transalgebraic class is a topological multiplicative group. We extend the action of the eñe product to the transcendental class on the Riemann sphere. This transalgebraic class, modulo constant functions, is a commutative ring for the multiplication, as the additive structure, and the eñe product, as the multiplicative structure. In particular, the divisor action of the eñe product by multiplicative convolution extends to these transalgebraic divisors. The polylogarithm hierarchy appears related to transalgebraic eñe poles of higher order.
Source: arXiv (Cornell University)
Author: Pérez-Marco, Ricardo
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2996672967