@unpublished{60474,
author = {{Januszewski, Fabian}},
booktitle = {{arXiv:2506.23251}},
pages = {{38}},
title = {{{Rational structures on quivers and a generalization of Gelfand's equivalence}}},
year = {{2025}},
}
@inproceedings{53194,
author = {{Januszewski, Fabian}},
booktitle = {{Proceedings of the 15-th International Workshop "Lie Theory and Its Applications in Physics" (LT-15), (19-25 June 2023, Varna, Bulgaria)}},
editor = {{Dobrev, Vladimir}},
issn = {{2194-1009}},
pages = {{10}},
publisher = {{Springer}},
title = {{{Families of D-modules and integral models of (g, K)-modules}}},
year = {{2024}},
}
@article{53190,
abstract = {{We prove new congruences between special values of Rankin-Selberg
$L$-functions for $\mathrm{GL}(n+1)\times\mathrm{GL}(n)$ over arbitrary number
fields. This allows us to control the behavior of $p$-adic $L$-functions under
Tate twists and to prove the existence of non-abelian $p$-adic $L$-functions
for Hida families on $\mathrm{GL}(n+1)\times\mathrm{GL}(n)$. As an application,
we prove strong non-vanishing results for central $L$-values: We give
sufficient local conditions for twisted central Rankin-Selberg $L$-values to be
generically non-zero.}},
author = {{Januszewski, Fabian}},
issn = {{0002-9327}},
journal = {{American Journal of Mathematics}},
number = {{2}},
pages = {{495--578}},
publisher = {{Johns Hopkins University, Johns Hopkins University Press}},
title = {{{Non-abelian $p$-adic Rankin-Selberg $L$-functions and non-vanishing of central $L$-values}}},
volume = {{146}},
year = {{2024}},
}
@unpublished{53197,
abstract = {{This paper introduces the notion of locally algebraic representations and corresponding sheaves in the context of the cohomology of arithmetic groups. These representations are particularly relevant for studying integral structures and special values of cohomological automorphic representations, as well as corresponding period relations. We introduce and investigate related concepts such as locally algebraic $(\lieg,K)$-modules and cohomological types of automorphic representations. Applying the recently developed theory of tdos and twisted $\mathcal D$-modules, we establish the existence of canonical global $1/N$-integral structures on spaces of automorphic cusp forms. As an application, we define canonical periods attached to regular algebraic automorphic representations, potentially related to the action of Venkatesh's derived Hecke algebra on cuspidal cohomology.}},
author = {{Januszewski, Fabian}},
booktitle = {{arXiv:2404.03955}},
pages = {{69}},
title = {{{Locally algebraic representations and integral structures on the cohomology of arithmetic groups}}},
year = {{2024}},
}
@unpublished{53195,
abstract = {{We develop a theory of tdos and twisted $\mathcal D$-modules over general
bases with an emphasis on functorial aspects. In particular, we establish a
flat base change theorem as well as faithfully flat descent for twisted
$\mathcal D$-modules. We define (derived) inverse and direct images of twisted
$\mathcal D$-modules and investigate how these functors behave under base
change. We also discuss forms of closed $K$-orbits attached to $\theta$-stable
parabolic subgroups. These results imply the existence of models of
cohomologically induced modules over general fields of characteristic 0 and
even half-integer rings, whose study is motivated by potential applications to
number theory in the literature.}},
author = {{Hayashi, Takuma and Januszewski, Fabian}},
booktitle = {{arXiv:1808.10709}},
pages = {{170}},
title = {{{Families of twisted D-modules and arithmetic models of Harish-Chandra modules}}},
year = {{2023}},
}
@article{53192,
abstract = {{The principal aim of this article is to attach and study $p$-adic $L$-functions to cohomological cuspidal automorphic representations $\Pi$ of $\operatorname {GL}_{2n}$ over a totally real field $F$ admitting a Shalika model. We use a modular symbol approach, along the global lines of the work of Ash and Ginzburg, but our results are more definitive because we draw heavily upon the methods used in the recent and separate works of all three authors. By construction, our $p$-adic $L$-functions are distributions on the Galois group of the maximal abelian extension of $F$ unramified outside $p\infty$. Moreover, we work under a weaker Panchishkine-type condition on $\Pi _p$ rather than the full ordinariness condition. Finally, we prove the so-called Manin relations between the $p$-adic $L$-functions at all critical points. This has the striking consequence that, given a unitary $\Pi$ whose standard $L$-function admits at least two critical points, and given a prime $p$ such that $\Pi _p$ is ordinary, the central critical value $L(\frac {1}{2}, \Pi \otimes \chi )$ is non-zero for all except finitely many Dirichlet characters $\chi$ of $p$-power conductor.}},
author = {{Dimitrov, Mladen and Januszewski, Fabian and Raghuram, A.}},
issn = {{0010-437X}},
journal = {{Compositio Mathematica}},
keywords = {{Algebra and Number Theory}},
number = {{12}},
pages = {{2437--2468}},
publisher = {{Wiley}},
title = {{{L-functions of GL(2n): p-adic properties and non-vanishing of twists}}},
doi = {{10.1112/s0010437x20007551}},
volume = {{156}},
year = {{2021}},
}
@article{53199,
author = {{Januszewski, Fabian}},
issn = {{0942-5977}},
journal = {{Mitteilungen der Deutschen Mathematiker-Vereinigung}},
keywords = {{Earth-Surface Processes}},
number = {{2}},
pages = {{68--72}},
publisher = {{Walter de Gruyter GmbH}},
title = {{{Von ganzen Zahlen zu L-Funktionen}}},
doi = {{10.1515/dmvm-2021-0027}},
volume = {{29}},
year = {{2021}},
}
@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{53189,
author = {{Januszewski, Fabian}},
issn = {{0025-5831}},
journal = {{Mathematische Annalen}},
keywords = {{General Mathematics}},
number = {{3-4}},
pages = {{1805--1881}},
publisher = {{Springer Science and Business Media LLC}},
title = {{{Rational structures on automorphic representations}}},
doi = {{10.1007/s00208-017-1567-6}},
volume = {{370}},
year = {{2017}},
}
@article{53188,
author = {{Januszewski, Fabian}},
issn = {{2195-4755}},
journal = {{Annales mathématiques du Québec; Special Issue in Honor of Glenn Stevens}},
keywords = {{General Mathematics}},
number = {{2}},
pages = {{453--489}},
publisher = {{Springer Science and Business Media LLC}},
title = {{{p-adic L-functions for Rankin–Selberg convolutions over number fields}}},
doi = {{10.1007/s40316-016-0061-y}},
volume = {{40}},
year = {{2016}},
}
@unpublished{53196,
abstract = {{We study Hecke algebras for pairs $({\mathfrak g},K)$ over arbitrary fields
$E$ of characteristic $0$, define the Bernstein functor and give another
definition of the Zuckerman functor over $E$. Building on this and the author's
previous work on rational structures on automorphic representations, we show
that hard duality remains valid over $E$ and apply this result to the study of
rationality properties of Sun's cohomologically induced functionals. Our main
application are period relations for the special values of standard
$L$-functions of automorphic representations of $\mathrm{GL}(2n)$ admitting
Shalika models.}},
author = {{Januszewski, Fabian}},
booktitle = {{arXiv:1604.04253}},
pages = {{65}},
title = {{{On Period Relations for Automorphic L-functions II}}},
year = {{2016}},
}
@misc{59180,
author = {{Januszewski, Fabian}},
title = {{{On Deligne's Conjecture on Special Values of L-functions}}},
year = {{2015}},
}
@article{53187,
author = {{Januszewski, Fabian}},
issn = {{0949–5932}},
journal = {{Journal of Lie Theory}},
pages = {{1161--1206}},
publisher = {{Heldermann Verlag}},
title = {{{Algebraic Characters of Harish-Chandra modules}}},
volume = {{24}},
year = {{2014}},
}
@article{53185,
author = {{Januszewski, Fabian}},
issn = {{1073-7928}},
journal = {{International Mathematics Research Notices}},
keywords = {{General Mathematics}},
number = {{17}},
pages = {{7884--7949}},
publisher = {{Oxford University Press (OUP)}},
title = {{{On p-adic L-functions for GL(n) × GL (n-1) over totally real fields}}},
doi = {{10.1093/imrn/rnu181}},
volume = {{2015}},
year = {{2014}},
}
@unpublished{53186,
abstract = {{These are expanded notes from lectures at the Workshop "Representation Theory
and Applications" held at Yeditepe University, Istanbul, in honor of Roger E.
Howe. They are supplemented by the application of algebraic character theory to
the construction of Galois-equivariant characters for Harish-Chandra modules.}},
author = {{Januszewski, Fabian}},
booktitle = {{arXiv:1310.6884}},
title = {{{Algebraic Characters of Harish-Chandra modules and arithmeticity}}},
year = {{2013}},
}
@article{53184,
author = {{Januszewski, Fabian}},
issn = {{0075-4102}},
journal = {{Journal für die reine und angewandte Mathematik (Crelles Journal)}},
keywords = {{Applied Mathematics, General Mathematics}},
number = {{653}},
pages = {{1--45}},
publisher = {{Walter de Gruyter GmbH}},
title = {{{Modular symbols for reductive groups and p-adic Rankin–Selberg convolutions over number fields}}},
doi = {{10.1515/crelle.2011.018}},
volume = {{2011}},
year = {{2010}},
}
@phdthesis{53183,
author = {{Januszewski, Fabian}},
isbn = {{978-3-86644-373-0}},
pages = {{ VI, 92 S.}},
publisher = {{KIT Scientific Publishing, 2009}},
title = {{{p-adische Rankin-Selberg-Faltungen}}},
doi = {{10.5445/KSP/1000011510}},
year = {{2009}},
}
@inbook{53181,
author = {{Geiselmann, Willi and Januszewski, Fabian and Köpfer, Hubert and Pelzl, Jan and Steinwandt, Rainer}},
booktitle = {{Information Security and Cryptology – ICISC 2006}},
isbn = {{9783540491125}},
issn = {{0302-9743}},
publisher = {{Springer Berlin Heidelberg}},
title = {{{A Simpler Sieving Device: Combining ECM and TWIRL}}},
doi = {{10.1007/11927587_12}},
year = {{2006}},
}