Baker-Type Estimates for Linear Forms in the Values of q-series

TL;DR

This paper develops Baker-type estimates for linear forms in the values of generalized Heine series at points in imaginary quadratic fields, providing bounds that depend on individual coefficients rather than just their maximum.

Contribution

It introduces a new Baker-type linear independence measure for q-series values in imaginary quadratic fields, emphasizing coefficient-dependent bounds.

Findings

Established a Baker-type linear independence measure for generalized Heine series.

Bounded linear forms based on individual coefficients, not just their maxima.

Enhanced understanding of q-series values in algebraic number fields.

Abstract

A Baker-type linear independece measure is obtained for the values of generalized Heine series at non-zero points of an imaginary quadratic number field. This kind of estimate depends on the individual coefficients of the linear form, not only on the maximum of their absolute values.