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Zeta values in Tate algebras were introduced by Pellarin in 2012. They are generalizations of Carlitz's zeta values and play an increasingly important role in function field arithmetic. In this… Click to show full abstract
Zeta values in Tate algebras were introduced by Pellarin in 2012. They are generalizations of Carlitz's zeta values and play an increasingly important role in function field arithmetic. In this paper, we prove a conjecture of Pellarin on identities for these zeta values. The proof is based on arithmetic properties of Carlitz's zeta values and an explicit formula for Bernoulli-type polynomials attached to Pellarin's zeta values.
Keywords:
identities zeta;
values tate;
tate algebras;
zeta values
Journal Title: Transactions of the American Mathematical Society
Year Published: 2020
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Journal Title: Transactions of the American Mathematical Society
Year Published: 2020
Link to full text (if available)
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recommendations!