Values of certain L-series in positive characteristic

By F. Pellarin. 2011

100 citations recorded by the source corpus.

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 !. We discuss how our formulas may be used to investigate the existence of a kind of functional equation for the Goss zeta function.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/5925698cb8d97214211277e2cad2dcbcf71fc336

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In Algebra and Number Theory

1. Bruno Anglès
2. Floric Tavares-Ribeiro
3. F. Pellarin

In Geometry and Topology

1. Bruno Anglès
2. Floric Tavares-Ribeiro
3. F. Pellarin

In Mathematical Physics

1. Bruno Anglès
2. Floric Tavares-Ribeiro
3. F. Pellarin

Citations in the corpus

• Arithmetic of positive characteristic $L$-series values in Tate algebras (2014, methodology): “177], was also used extensively in [15, 4].”
• Universal Gauss-Thakur sums and $$L$$L-series (2013, background): “In [12], the second author introduced a class of L-series which analytically interpolate the Carlitz zeta values and the special values of Dirichlet-Goss L-series.”