@article{60993,
abstract = {{We determine the distribution of discriminants of wildly ramified elementary-abelian extensions of local and global function fields in characteristic
p
p
. For local and rational function fields, we also give precise formulae for the number of elementary-abelian extensions with a fixed discriminant divisor, which describe a local-global principle.
}},
author = {{Potthast, Nicolas}},
issn = {{1088-6850}},
journal = {{Transactions of the American Mathematical Society}},
number = {{1}},
pages = {{289 -- 340}},
publisher = {{American Mathematical Society (AMS)}},
title = {{{On the asymptotics of elementary-abelian extensions of local and global function fields}}},
doi = {{10.1090/tran/9509}},
volume = {{379}},
year = {{2026}},
}
@article{53191,
abstract = {{This paper is the first in a series of two dedicated to the study of period relations of the type
L
(
1
2
+
k
,
Π
)
∈
(
2
π
i
)
d
⋅
k
Ω
(
−
1
)
k
\bf Q
(
Π
)
,
1
2
+
k
critical
,
\begin{equation*} L\Big (\frac {1}{2}+k,\Pi \Big )\;\in \;(2\pi i)^{d\cdot k}\Omega _{(-1)^k}\textrm {\bf Q}(\Pi ),\quad \frac {1}{2}+k\;\text {critical}, \end{equation*}
for certain automorphic representations
Π
\Pi
of a reductive group
G
.
G.
In this paper we discuss the case
G
=
G
L
(
n
+
1
)
×
G
L
(
n
)
.
G=\mathrm {GL}(n+1)\times \mathrm {GL}(n).
The case
G
=
G
L
(
2
n
)
G=\mathrm {GL}(2n)
is discussed in part two. Our method is representation theoretic and relies on the author’s recent results on global rational structures on automorphic representations. We show that the above period relations are intimately related to the field of definition of the global representation
Π
\Pi
under consideration. The new period relations we prove are in accordance with Deligne’s Conjecture on special values of
L
L
-functions, and the author expects this method to apply to other cases as well.
}},
author = {{Januszewski, Fabian}},
issn = {{0002-9947}},
journal = {{Transactions of the American Mathematical Society}},
keywords = {{Applied Mathematics, General Mathematics}},
number = {{9}},
pages = {{6547--6580}},
publisher = {{American Mathematical Society (AMS)}},
title = {{{On period relations for automorphic 𝐿-functions I}}},
doi = {{10.1090/tran/7527}},
volume = {{371}},
year = {{2018}},
}
@article{64666,
author = {{Glöckner, Helge and Lucht, Lutz G.}},
issn = {{0002-9947}},
journal = {{Transactions of the American Mathematical Society}},
keywords = {{11M41, 30B50, 30J99, 46H99}},
number = {{6}},
pages = {{3275–3293}},
title = {{{Weighted inversion of general Dirichlet series}}},
doi = {{10.1090/S0002-9947-2013-06018-7}},
volume = {{366}},
year = {{2014}},
}