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ABEL ARITHMETIC FUNCTIONS IN FINITE CHARACTERISTIC

Abstract : We define Abel arithmetic functions in function fields with positive characteristic. We prove that any Abel arithmetic function with exponential type lesser than [Formula: see text] is a polynomial, the bound [Formula: see text] being optimal. This provides an analog of a Bertrandias' result. Some q-analogs are considered too.
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Submitted on : Friday, November 5, 2021 - 10:59:54 PM
Last modification on : Monday, November 15, 2021 - 7:30:02 PM

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David Adam. ABEL ARITHMETIC FUNCTIONS IN FINITE CHARACTERISTIC. International Journal of Number Theory, World Scientific Publishing, 2012, 08 (06), pp.1557-1568. ⟨10.1142/S1793042112500959⟩. ⟨hal-03417874⟩

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