Artin Conjecture for p-adic Galois Representations of Function Fields

For a global function field K of positive characteristic p, we show that Artin conjecture for L-functions of geometric p-adic Galois representations of K is true in a non-trivial p-adic disk but is false in the full p-adic plane. In particular, we prove the non-rationality of the geometric unit root L-functions.Comment: Remove the condition 6|k in Lemma 3.8; final versio

T-adic exponential sums over finite fields

$T$-adic exponential sums associated to a Laurent polynomial $f$ are introduced. They interpolate all classical $p^m$-power order exponential sums associated to $f$. The Hodge bound for the Newton polygon of $L$-functions of $T$-adic exponential sums is established. This bound enables us to determine, for all $m$, the Newton polygons of $L$-functions of $p^m$-power order exponential sums associated to an $f$ which is ordinary for $m=1$. Deeper properties of $L$-functions of $T$-adic exponential sums are also studied. Along the way, new open problems about the $T$-adic exponential sum itself are discussed.Comment: new version, 21 pages, title is changed to

A Text Mining and Ensemble Learning Based Approach for Credit Risk Prediction

Traditional credit risk prediction models mainly rely on financial data. However, technological innovation is the main driving force for the development of enterprises in strategic emerging industries, which is closely related to enterprise credit risk. In this paper, a novel prediction framework utilizing technological innovation text mining data and ensemble learning is proposed. The empirical data from China listed enterprises in strategic emerging industries were applied to construct prediction models using the classification and regression tree model, the random forest model and extreme gradient boosting model. The results show that the model uses the technological innovation text mining data proven to have significant predict ability, and top management teamꞌs attention to innovation variables offer the best prediction capacities. This work improves the application value of enterprise credit risk prediction models in strategic emerging industries by embedding the mining of technological innovation text information