Multiplicity estimate for solutions of extended Ramanujan's system

TL;DR

This paper introduces a new multiplicity lemma for solutions to an extended Ramanujan differential system, aiming to advance understanding of the arithmetic properties of zeta function values at odd integers.

Contribution

It presents a novel multiplicity lemma for an extended Ramanujan system, expanding tools for studying zeta function values.

Findings

Established a new multiplicity lemma for extended Ramanujan systems

Potential applications in studying arithmetic properties of zeta values

Provides a foundation for future research in transcendence and algebraic independence

Abstract

We establish a new multiplicity lemma for solutions of a differential system extending Ramanujan's classical differential relations. This result can be useful in the study of arithmetic properties of values of Riemann zeta function at odd positive integers (Nesterenko, 2011).