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Concept

Théorie algébrique des nombres

Publications associées (22)

Algebraic twists of GL(2) automorphic forms

Vignesh Arumugam Nadarajan

In this thesis we consider the problem of estimating the correlation of Hecke eigenvalues of GL2 automorphic forms with a class of functions of algebraic origin defined over finite fields called trace functions. The class of trace functions is vast and inc ...

EPFL2023

A Hopf algebra model for Dwyer's tame spaces

Haoqing Wu

In this thesis, we give a modern treatment of Dwyer's tame homotopy theory using the language of

\infty

-categories. We introduce the notion of tame spectra and show it has a concrete algebraic description. We then carry out a study of

\infty

-operads an ...

EPFL2022

Fourier uniqueness and interpolation in Euclidean space

Martin Peter Stoller

We prove that every Schwartz function in Euclidean space can be completely recovered given only its restrictions and the restrictions of its Fourier transform to all origin-centered spheres whose radii are square roots of integers. In particular, the only ...

EPFL2022

A Shadow Perspective on Equivariant Hochschild Homologies

Kathryn Hess Bellwald

Shadows for bicategories, defined by Ponto, provide a useful framework that generalizes classical and topological Hochschild homology. In this paper, we define Hochschild-type invariants for monoids in a symmetric monoidal, simplicial model category V, as ...

OXFORD UNIV PRESS2022

Petersson inner products of weight-one modular forms

Maryna Viazovska

In this paper we study the regularized Petersson product between a holomorphic theta series associated to a positive definite binary quadratic form and a weakly holomorphic weight-one modular form with integral Fourier coefficients. In [18], we proved that ...

2019

Non-uniqueness of admissible weak solutions to the Riemann problem for isentropic Euler equations

Elisabetta Chiodaroli

We study the Riemann problem for multidimensional compressible isentropic Euler equations. Using the framework developed in Chiodaroli et al (2015 Commun. Pure Appl. Math. 68 1157-90), and based on the techniques of De Lellis and Szekelyhidi (2010 Arch. Ra ...

IOP PUBLISHING LTD2018

Some remarks on rearrangement for nonlocal functionals

Hoài-Minh Nguyên

We prove that a nonlocal functional approximating the standard Dirichlet p-norm fails to decrease under two-point rearrangement. Furthermore, we get other properties related to this functional such as decay and compactness. ...

2017

Large Sieve Inequalities for Algebraic Trace Functions

Philippe Michel, Ping Xi

The large sieve inequalities for algebraic trace functions are considered in this article. A fundamental iterative relation is established by classical Fourier analysis, and l-adic Fourier analysis and multiplicative convolutions of sheaves are also requir ...

Oxford Univ Press2017

Erdos Distinct Distances Problem and Extensions over Finite Spaces

Van Thang Pham

In this thesis we study a number of problems in Discrete Combinatorial Geometry in finite spaces. The contents in this thesis are structured as follows: In Chapter 1 we will state the main results and the notations which will be used throughout the thesis. ...

EPFL2017

MRI artifact correction using sparse plus low-rank decomposition of annihilating filter-based hankel matrix

Kyong Hwan Jin

PurposeMagnetic resonance imaging (MRI) artifacts are originated from various sources including instability of an magnetic resonance (MR) system, patient motion, inhomogeneities of gradient fields, and so on. Such MRI artifacts are usually considered as ir ...

Wiley2017

Computational Aspects of Jacobians of Hyperelliptic Curves

Alina Dudeanu

Nowadays, one area of research in cryptanalysis is solving the Discrete Logarithm Problem (DLP) in finite groups whose group representation is not yet exploited. For such groups, the best one can do is using a generic method to attack the DLP, the fastest ...

EPFL2016

Hybrid Bounds For Automorphic Forms On Ellipsoids Over Number Fields

Philippe Michel

We prove upper bounds for Hecke-Laplace eigenfunctions on certain Riemannian manifolds X of arithmetic type, uniformly in the eigenvalue and the volume of the manifold. The manifolds under consideration are d-fold products of 2-spheres or 3-spheres, realiz ...

Cambridge Univ Press2013

Algebraic Divisibility Sequences Over Function Fields

In this note we study the existence of primes and of primitive divisors in function field analogues of classical divisibility sequences. Under various hypotheses, we prove that Lucas sequences and elliptic divisibility sequences over function fields define ...

Australian Mathematical Society2012

Hermitian Forms over Algebras with Involution and Hermitian Categories

Daniel Arnold Moldovan

This thesis is concerned with the algebraic theory of hermitian forms. It is organized in two parts. The first, consisting of the first two chapters, deals with some descent properties of unimodular hermitian forms over central simple algebras with involut ...

EPFL2012

Primeless Modular Cryptography (Extended Abstract)

Serge Vaudenay, Sonia Mihaela Bogos, Ioana Cristina Carlson

Most of the known public-key cryptosystems have an overall complexity which is dominated by the key-production algorithm, which requires the generation of prime numbers. This is most inconvenient in settings where the key-generation is not an one-off proce ...

2012

What are the Longest Ropes on the Unit Sphere?

We consider the variational problem of finding the longest closed curves of given minimal thickness on the unit sphere. After establishing the existence of solutions for any given thickness between 0 and 1, we explicitly construct for each given thickness ...

Springer-Verlag2011

A general framework for homotopic descent and codescent

Kathryn Hess Bellwald

In this paper we elaborate a general homotopy-theoretic framework in which to study problems of descent and completion and of their duals, codescent and cocompletion. Our approach to homotopic (co)descent and to derived (co)completion can be viewed as $\in ...

2010

Annihilating Polynomials for Quadratic Forms

Let K be a field with char(K) ≠ 2. The Witt-Grothendieck ring (K) and the Witt ring W (K) of K are both quotients of the group ring ℤ[𝓖(K)], where 𝓖(K) := K*/(K*)2 is the square class group of K. Since ℤ[𝓖(K)] is integra ...

EPFL2010

Catégories simpliciales enrichies et K-théorie de Waldhausen

Ilias Amrani

This thesis, which presents a new approach to the algebraic K-theory, is divided into two parts. The first one is devoted to the category of small simplicial categories. First, we construct a new model structure on sCat = [Δop,Cat] which is called the diag ...

EPFL2010

Arithmetic Bounds-Lenstra's Constant and Torsion of K-Groups

This thesis is concerned with computations of bounds for two different arithmetic invariants. In both cases it is done with the intention of proving some algebraic or arithmetic properties for number fields. The first part is devoted to computations of low ...

EPFL2010

Publications associées (22)

Algebraic twists of GL(2) automorphic forms

Vignesh Arumugam Nadarajan

EPFL2023

A Hopf algebra model for Dwyer's tame spaces

Haoqing Wu

In this thesis, we give a modern treatment of Dwyer's tame homotopy theory using the language of

\infty

-categories. We introduce the notion of tame spectra and show it has a concrete algebraic description. We then carry out a study of

\infty

-operads an ...

EPFL2022