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arXiv · 2005.13903

Special values of Goss $L$-series attached to Drinfeld modules of rank 2

Oguz Gezmis
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Abstract

Inspired by the classical setting, Goss defined $L$-series attached to Drinfeld modules. In this paper, for a fixed choice of a power $q$ of a prime number and a given Drinfeld module $\phi$ of rank 2 with a certain condition on its coefficients, we give explicit formulas for the values of Goss $L$-series attached to $\phi$ at positive integers $n$ such that $2n+1\leq q$ in terms of polylogarithms and coefficients of the logarithm series of $\phi$.

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Oguz Gezmis. 2020-05-28. Special values of Goss $L$-series attached to Drinfeld modules of rank 2. https://arxiv.org/abs/2005.13903

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