Higher Hida theory and p-adic L-functions for
D Loeffler, V Pilloni, C Skinner… - Duke Mathematical …, 2021 - projecteuclid.org
We use the “higher Hida theory” recently introduced by the second author to p-adically
interpolate periods of nonholomorphic automorphic forms for GSp 4, contributing to coherent …
interpolate periods of nonholomorphic automorphic forms for GSp 4, contributing to coherent …
A spectral reciprocity formula and non-vanishing for L-functions on GL (4)× GL (2)
V Blomer, X Li, SD Miller - Journal of Number Theory, 2019 - Elsevier
We introduce a new type of summation formula for central values of GL (4)× GL (2) L-
functions, when varied over Maaß forms. By rewriting such a sum in terms of GL (4)× GL (1) …
functions, when varied over Maaß forms. By rewriting such a sum in terms of GL (4)× GL (1) …
On the Bloch-Kato conjecture for GSp (4)
D Loeffler, SL Zerbes - arXiv preprint arXiv:2003.05960, 2020 - arxiv.org
We prove an explicit reciprocity law for the Euler system attached to the spin motive of a
genus 2 Siegel modular form. As consequences, we obtain one inclusion of the Iwasawa …
genus 2 Siegel modular form. As consequences, we obtain one inclusion of the Iwasawa …
Spherical varieties and norm relations in Iwasawa theory
D Loeffler - Journal de théorie des nombres de Bordeaux, 2021 - numdam.org
Norm-compatible families of cohomology classes for Shimura varieties, and other arithmetic
symmetric spaces, play an important role in Iwasawa theory of automorphic forms. The aim …
symmetric spaces, play an important role in Iwasawa theory of automorphic forms. The aim …
On -adic -functions for in finite slope Shalika families
DB Salazar, M Dimitrov, C Williams - arXiv preprint arXiv:2103.10907, 2021 - arxiv.org
In this paper, we prove new results on the geometry of the cuspidal eigenvariety for
$\mathrm {GL} _ {2n} $ over a totally real number field $ F $ at classical points admitting …
$\mathrm {GL} _ {2n} $ over a totally real number field $ F $ at classical points admitting …
Non-abelian -adic Rankin-Selberg -functions and non-vanishing of central -values
F Januszewski - arXiv preprint arXiv:1708.02616, 2017 - arxiv.org
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 …
$\mathrm {GL}(n+ 1)\times\mathrm {GL}(n) $ over arbitrary number fields. This allows us to …
On the Birch-Swinnerton-Dyer conjecture for modular abelian surfaces
D Loeffler, SL Zerbes - arXiv preprint arXiv:2110.13102, 2021 - arxiv.org
Let $ A $ be a modular abelian surface over $ Q $ which either has trivial geometric
endomorphism ring, or arises as the restriction of scalars of an elliptic curve over an …
endomorphism ring, or arises as the restriction of scalars of an elliptic curve over an …
Anticyclotomic Euler systems for unitary groups
A Graham, SWA Shah - Proceedings of the London …, 2023 - Wiley Online Library
Anticyclotomic Euler systems for unitary groups - Graham - 2023 - Proceedings of the London
Mathematical Society - Wiley Online Library Skip to Article Content Skip to Article Information …
Mathematical Society - Wiley Online Library Skip to Article Content Skip to Article Information …
On the GL(2n) eigenvariety: branching laws, Shalika families and -adic -functions
DB Salazar, M Dimitrov, A Graham, A Jorza… - arXiv preprint arXiv …, 2022 - arxiv.org
In this paper, we prove that a GL (2n)-eigenvariety is etale over the (pure) weight space at
non-critical Shalika points, and construct multi-variabled $ p $-adic $ L $-functions varying …
non-critical Shalika points, and construct multi-variabled $ p $-adic $ L $-functions varying …
P-adic L-functions for GL (3)
D Loeffler, C Williams - arXiv preprint arXiv:2111.04535, 2021 - arxiv.org
Let $\Pi $ be a regular algebraic cuspidal automorphic representation of $\mathrm {GL} _3
(\mathbb {A} _ {\mathbb {Q}}) $. When $\Pi $ is $ p $-ordinary for the maximal standard …
(\mathbb {A} _ {\mathbb {Q}}) $. When $\Pi $ is $ p $-ordinary for the maximal standard …