SPECIAL VALUES OF L-SERIES OVER TATE ALGEBRAS
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Date
2019-07-11
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Abstract
In this work, we investigate Taelman L-values corresponding to Drinfeld modules over Tate algebras of arbitrary rank. Furthermore, we give log-algebraicity results which can be seen as an n-variable version of a log-algebraicity result of Chang, El-Guindy and Papanikolas.
Moreover we introduce vanishing criteria for power sums twisted by the function µ depending on the coefficients of the Drinfeld module. We also introduce a Pellarin-type L-series converging in Tate algebras which take Taelman L-values as one of its special values and prove its analytic continuation to the topological group S∞ introduced by Goss.
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Drinfeld modules, Tate algebras, L-series