Publications associées à A finiteness result for p-adic families of Bianchi modular forms

Publications associées (33)

Local monodromy of Drinfeld modules

Compared with algebraic varieties the local monodromy of Drinfeld modules appears to be hopelessly complex: the image of the wild inertia subgroup under Tate module representations is infinite save for the case of potential good reduction. Nonetheless, we ...

CAMBRIDGE UNIV PRESS2024

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 ...

Hebrew Univ Magnes Press2023

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

Byzantine consensus is Θ(n^2): the Dolev-Reischuk bound is tight even in partial synchrony!

Rachid Guerraoui, Vincent Gramoli, Seth Gilbert, Jovan Komatovic, Manuel José Ribeiro Vidigueira, Pierre Philippe Civit

The Dolev-Reischuk bound says that any deterministic Byzantine consensus protocol has (at least) quadratic (in the number of processes) communication complexity in the worst case: given a system with n processes and at most f < n/3 failures, any solution t ...

2023

Coxeter Combinatorics For Sum Formulas In The Representation Theory Of Algebraic Groups

Jonathan Gruber

Let G be a simple algebraic group over an algebraically closed field F of characteristic p >= h, the Coxeter number of G. We observe an easy 'recursion formula' for computing the Jantzen sum formula of a Weyl module with p-regular highest weight. We also d ...

AMER MATHEMATICAL SOC2022

Zero-Knowledge IOPs with Linear-Time Prover and Polylogarithmic-Time Verifier

Alessandro Chiesa

Interactive oracle proofs (IOPs) are a multi-round generalization of probabilistically checkable proofs that play a fundamental role in the construction of efficient cryptographic proofs. ...

SPRINGER INTERNATIONAL PUBLISHING AG2022

Multiplicity-free representations of algebraic groups II

Donna Testerman

We continue our work, started in [9], on the program of classifying triples (X, Y, V), where X, Yare simple algebraic groups over an algebraically closed field of characteristic zero with X < Y, and Vis an irreducible module for Y such that the restriction ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2022

Computation Of A 30750-Bit Binary Field Discrete Logarithm

Arjen Lenstra, Thorsten Kleinjung, Robert Granger, Benjamin Pierre Charles Wesolowski

This paper reports on the computation of a discrete logarithm in the finite field F-230750, breaking by a large margin the previous record, which was set in January 2014 by a computation in F-29234. The present computation made essential use of the elimina ...

AMER MATHEMATICAL SOC2021

A probabilistic finite element method based on random meshes: A posteriori error estimators and Bayesian inverse problems

Assyr Abdulle, Giacomo Garegnani

We present a novel probabilistic finite element method (FEM) for the solution and uncertainty quantification of elliptic partial differential equations based on random meshes, which we call random mesh FEM (RM-FEM). Our methodology allows to introduce a pr ...

ELSEVIER SCIENCE SA2021

The fourth moment of individual Dirichlet L-functions on the critical line

Berke Topacogullari

We prove an asymptotic formula for the second moment of a product of two Dirichlet L-functions on the critical line, which has a power saving in the error term and which is uniform with respect to the involved Dirichlet characters. As special cases we give ...

2021

Fast assembly of Galerkin matrices for 3D solid laminated composites using finite element and isogeometric discretizations

Pablo Antolin Sanchez

This work presents a novel methodology for speeding up the assembly of stiffness matrices for laminate composite 3D structures in the context of isogeometric and finite element discretizations. By splitting the involved terms into their in-plane and out-of ...

2020

Efficient Verifiable Delay Functions

Benjamin Pierre Charles Wesolowski

We construct a verifiable delay function (VDF). A VDF is a function whose evaluation requires running a given number of sequential steps, yet the result can be efficiently verified. They have applications in decentralised systems, such as the generation of ...

SPRINGER INTERNATIONAL PUBLISHING AG2019

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

Adaptive Majority Problems For Restricted Query Graphs And For Weighted Sets

Doemoetoer Palvoelgyi, Abhishek Methuku, Balázs Keszegh

Suppose that the vertices of a graph G are colored with two colors in an unknown way. The color that occurs on more than half of the vertices is called the majority color (if it exists), and any vertex of this color is called a majority vertex. We study th ...

COMENIUS UNIV2019

Beyond Conventional Security in Sponge-Based Authenticated Encryption Modes

Philipp Svetolik Jovanovic

The Sponge function is known to achieve 2c/2 security, where c is its capacity. This bound was carried over to its keyed variants, such as SpongeWrap, to achieve a min{2c/2,2 kappa} security bound, with kappa the key length. Similarly, many CAESAR competit ...

SPRINGER2019

Arithmetic and geometric structures in cryptography

Benjamin Pierre Charles Wesolowski

We explore a few algebraic and geometric structures, through certain questions posed by modern cryptography. We focus on the cases of discrete logarithms in finite fields of small characteristic, the structure of isogeny graphs of ordinary abelian varietie ...

EPFL2018

Four-Variable Expanders Over The Prime Fields

Van Thang Pham, Adrian Claudiu Valculescu, Seyed Hossein Nassajianmojarrad

Let F-p be a prime field of order p > 2, and let A be a set in F-p with very small size in terms of p. In this note, we show that the number of distinct cubic distances determined by points in A x A satisfies vertical bar(A - A)(3) + (A - A)(3 vertical bar ...

American Mathematical Society (AMS)2018

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

Bilinear forms with Kloosterman sums and applications

Philippe Michel

We prove nontrivial bounds for general bilinear forms in hyper-Kloosterman sums when the sizes of both variables may be below the range controlled by Fourier-analytic methods (Polya-Vinogradov range). We then derive applications to the second moment of cus ...

Annal Mathematics2017

Quadratic Sieving

Thorsten Kleinjung

We propose an efficient variant for the initialisation step of quadratic sieving, the sieving step of the quadratic sieve and its variants, which is also used in sieving-based algorithms for computing class groups of quadratic fields. As an application we ...

American Mathematical Society2016