Values of certain L-series in positive characteristic

• 成果类型: Article
• 署名作者: Pellarin, Federico
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2012.176.3.13
• 发表日期: 2012
• 页码: 2055-2093
• 关键词: drinfeld modular-forms; a-harmonic series; function-fields; algebraic independence; motives

摘要

We introduce a class of deformations of the values of the Goss zeta function. We prove, with the use of the theory of deformations of vectorial modular forms as well as with other techniques, a formula for their value at 1, and some arithmetic properties of values at other positive integers. Our formulas involve Anderson and Thakur's function omega. We discuss how our formulas may be used to investigate the existence of a kind of functional equation for the Gosszeta function.