Results 1 to 10 of about 32 (24)

Application of automorphic forms to lattice problems

Journal of Mathematical Cryptology, 2022
In this article, we propose a new approach to the study of lattice problems used in cryptography. We specifically focus on module lattices of a fixed rank over some number field.
Düzlü Samed, Krämer Juliane
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EULER SYSTEMS FOR HILBERT MODULAR SURFACES

Forum of Mathematics, Sigma, 2018
We construct an Euler system—a compatible family of global cohomology classes—for the Galois representations appearing in the geometry of Hilbert modular surfaces.
ANTONIO LEI, DAVID LOEFFLER, SARAH LIVIA ZERBES   +2 more
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On Artin representations and nearly ordinary Hecke algebras over totally real fields

Documenta Mathematica, 2013
We prove many new cases of the strong Artin conjecture for two-dimensional, totally odd, insoluble (icosahedral) representations Gal(F/F ) → GL2(C) of the absolute Galois group of a totally real field F .
Shu Sasaki
semanticscholar   +1 more source

Modularity lifting results in parallel weight one and applications to the Artin conjecture: the tamely ramified case

Forum of Mathematics, Sigma, 2014
We extend the modularity lifting result of P. Kassaei (‘Modularity lifting in parallel weight one’,J. Amer. Math. Soc. 26 (1) (2013), 199–225) to allow Galois representations with some ramification at
PAYMAN L. KASSAEI, SHU SASAKI, YICHAO TIAN   +2 more
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UNRAMIFIEDNESS OF GALOIS REPRESENTATIONS ARISING FROM HILBERT MODULAR SURFACES

Forum of Mathematics, Sigma, 2017
Let $p$ be a prime number and $F$ a totally real number ...
MATTHEW EMERTON, DAVIDE REDUZZI, LIANG XIAO   +2 more
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Several variables $p$-adic $L$-functions for Hida families of Hilbert modular forms

Documenta Mathematica, 2012
After formulating Conjecture A for p-adic L-functions defined over ordinary Hilbert modular Hida deformations on a totally real field F of degree d, we construct two p-adic L-functions of d+1-variable depending on the parity of weight as a partial result
T. Ochiai
semanticscholar   +1 more source

Modularity of the Consani-Scholten quintic. With an appendix by José Burgos Gil and Ariel Pacetti

Documenta Mathematica, 2012
We prove that the Consani-Scholten quintic, a CalabiYau threefold over Q, is Hilbert modular. For this, we refine several techniques known from the context of modular forms.
L. Dieulefait, Ariel Pacetti, M. Schütt
semanticscholar   +1 more source

Deformations of Theta Integrals and A Conjecture of Gross-Zagier

Forum of Mathematics, Sigma
In this paper, we complete the proof of the conjecture of Gross and Zagier concerning algebraicity of higher Green functions at a single CM point on the product of modular curves. The new ingredient is an analogue of the incoherent Eisenstein series over
Jan H. Bruinier, Yingkun Li, Tonghai Yang   +2 more
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Kodaira–Spencer isomorphisms and degeneracy maps on Iwahori-level Hilbert modular varieties: the saving trace

Forum of Mathematics, Sigma
We consider integral models of Hilbert modular varieties with Iwahori level structure at primes over p, first proving a Kodaira–Spencer isomorphism that gives a concise description of their dualizing sheaves. We then analyze fibres of the degeneracy maps
Fred Diamond
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L-invariants for cohomological representations of PGL(2) over arbitrary number fields

Forum of Mathematics, Sigma
Let $\pi $ be a cuspidal, cohomological automorphic representation of an inner form G of $\operatorname {{PGL}}_2$ over a number field F of arbitrary signature. Further, let $\mathfrak {p}$ be a prime of F such that G is split at
Lennart Gehrmann, Maria Rosaria Pati
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