Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the transcendence of special values of Goss $L$-functions attached to
  Drinfeld modules   Let $\mathbb{F}_q$ be the finite field with $q$ elements and consider the
rational function field $K:=\mathbb{F}_q(\theta)$. For a Drinfeld module $\phi$
defined over $K$, we study the transcendence of special values of the Goss
$L$-function attached to the abelian $t$-motive $M_{\phi}$ of $\phi$. Moreover,
when $\phi$ is a Drinfeld module of rank $r\geq 2$ defined over $K$ which has
everywhere good reduction, we prove that the value of the Goss $L$-function
attached to the $(r-1)$-st exterior power of $M_{\phi}$ at any positive integer
is transcendental over $K$. As an application of our methods, we also prove the
transcendence of Taelman $L$-values of an explicit family of abelian
$t$-modules.

11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
20
The categories of this paper are: acc-phys
35
The categories of this paper are: mtrl-th
14
The categories of this paper are: math-ph
12
The categories of this paper are: nucl-th
16
The categories of this paper are: stat
22
The categories of this paper are: chao-dyn
26
The categories of this paper are: bayes-an
23
The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg