Publications related to Discriminant of an algebraic number field

K3 surfaces, cyclotomic polynomials and orthogonal groups

Let X be a complex projective K3 surface and let T-X be its transcendental lattice; the characteristic polynomials of isometries of T-X induced by automorphisms of X are powers of cyclotomic polynomials. Which powers of cyclotomic polynomials occur? The ai ...

Springer Int Publ Ag2024

NORM TORI OF ETALE ALGEBRAS AND UNRAMIFIED BRAUER GROUPS

Eva Bayer Fluckiger, Ting-Yu Lee

Let k be a field, and let L be an etale k-algebra of finite rank. If a is an element of k(x), let X-a be the affine variety defined by N-L/k(x) = a. Assuming that L has at least one factor that is a cyclic field extension of k, we give a combinatorial desc ...

Jerusalem2023

Lattice packings through division algebras

Nihar Prakash Gargava

In this text, we will show the existence of lattice packings in a family of dimensions by employing division algebras. This construction is a generalization of Venkatesh's lattice packing result Venkatesh (Int Math Res Notices 2013(7): 1628-1642, 2013). In ...

SPRINGER HEIDELBERG2023

Moments of the number of points in a bounded set for number field lattices

Maryna Viazovska, Nihar Prakash Gargava, Vlad Serban

We examine the moments of the number of lattice points in a fixed ball of volume

V

for lattices in Euclidean space which are modules over the ring of integers of a number field

K

. In particular, denoting by

ω_K

the number of roots of unity in

K

, we ...

arXiv2023

Short Stickelberger Class Relations and Application to Ideal-SVP

Benjamin Pierre Charles Wesolowski

The worst-case hardness of finding short vectors in ideals of cyclotomic number fields (Ideal-SVP) is a central matter in lattice based cryptography. Assuming the worst-case hardness of Ideal-SVP allows to prove the Ring-LWE and Ring-SIS assumptions, and t ...

Springer International Publishing Ag2017

Brain-actuated gait trainer with visual and proprioceptive feedback

José del Rocio Millán Ruiz, Mohamed Bouri, Kyuhwa Lee, Ricardo Andres Chavarriaga Lozano, Dong Liu

Objective. Brain-machine interfaces (BMIs) have been proposed in closed-loop applications for neuromodulation and neurorehabilitation. This study describes the impact of different feedback modalities on the performance of an EEG-based BMI that decodes moto ...

Institute of Physics2017

Inhomogeneous minima of mixed signature lattices

Eva Bayer Fluckiger, Martino Borello, Peter Simon Jossen

We establish an explicit upper bound for the Euclidean minimum of a number field which depends, in a precise manner, only on its discriminant and the number of real and complex embeddings. Such bounds were shown to exist by Davenport and Swinnerton-Dyer ([ ...

Academic Press Inc Elsevier Science2016

Shimura Curves and Special Values of p-adic L-functions

Ernest Hunter Brooks

We construct "generalized Heegner cycles" on a variety fibered over a Shimura curve, defined over a number field. We show that their images under the p-adic Abel-Jacobi map coincide with the values (outside the range of interpolation) of a p-adic L-functio ...

Oxford University Press2015

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Moments of the number of points in a bounded set for number field lattices

Maryna Viazovska, Nihar Prakash Gargava, Vlad Serban

We examine the moments of the number of lattice points in a fixed ball of volume

V

for lattices in Euclidean space which are modules over the ring of integers of a number field

K

. In particular, denoting by

ω_K

the number of roots of unity in

K

, we ...

arXiv2023

Discriminant of an algebraic number field

K3 surfaces, cyclotomic polynomials and orthogonal groups

NORM TORI OF ETALE ALGEBRAS AND UNRAMIFIED BRAUER GROUPS

Lattice packings through division algebras

Moments of the number of points in a bounded set for number field lattices

Algebraic twists of GL(2) automorphic forms

Petersson inner products of weight-one modular forms

Short Stickelberger Class Relations and Application to Ideal-SVP

Brain-actuated gait trainer with visual and proprioceptive feedback

Inhomogeneous minima of mixed signature lattices

Shimura Curves and Special Values of p-adic L-functions

Graph Chatbot

Chat with Graph Search

K3 surfaces, cyclotomic polynomials and orthogonal groups

NORM TORI OF ETALE ALGEBRAS AND UNRAMIFIED BRAUER GROUPS

Lattice packings through division algebras

Moments of the number of points in a bounded set for number field lattices

Algebraic twists of GL(2) automorphic forms

Petersson inner products of weight-one modular forms

Short Stickelberger Class Relations and Application to Ideal-SVP

Brain-actuated gait trainer with visual and proprioceptive feedback

Inhomogeneous minima of mixed signature lattices

Shimura Curves and Special Values of p-adic L-functions