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Eñe product in the transalgebraic class

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.
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Preprints, Working Papers, ...
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https://hal.archives-ouvertes.fr/hal-02417763
Contributor : Ricardo Pérez-Marco Connect in order to contact the contributor
Submitted on : Wednesday, December 18, 2019 - 1:32:22 PM
Last modification on : Saturday, December 4, 2021 - 4:05:14 AM
Long-term archiving on: : Thursday, March 19, 2020 - 8:19:31 PM

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  • HAL Id : hal-02417763, version 1

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Ricardo Pérez-Marco. Eñe product in the transalgebraic class. 2019. ⟨hal-02417763⟩

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