Publications related to Class number problem

Algebraic twists of GL(2) automorphic forms

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

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

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

Vlad Serban

We study p-adic families of cohomological automorphic forms for GL(2) over imaginary quadratic fields and prove that families interpolating a Zariski-dense set of classical cuspidal automorphic forms only occur under very restrictive conditions. We show ho ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2022

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 ...

2020

Relax and Recover: Guaranteed Range-Only Continuous Localization

Adam James Scholefield, Frederike Dümbgen, Michalina Wanda Pacholska

Range-only localization has applications as diverse as underwater navigation, drone tracking and indoor localization. While the theoretical foundations of lateration---range-only localization for static points---are well understood, there is a lack of unde ...

2020

Relax and Recover: Guaranteed Range-Only Continuous Localization

Adam James Scholefield, Frederike Dümbgen, Michalina Wanda Pacholska

Range-only localization has applications as diverse as underwater navigation, drone tracking and indoor localization. While the theoretical foundations of lateration-range-only localization for static points-are well understood, there is a lack of understa ...

2020

Matrix recovery from bilinear and quadratic measurements

Martin Vetterli, Adam James Scholefield, Michalina Wanda Pacholska, Karen Adam

Matrix (or operator) recovery from linear measurements is a well-studied problem. However, there are situations where only bilinear or quadratic measurements are available. A bilinear or quadratic problem can easily be transformed into a linear one, but it ...

ArXiv2020

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

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

Enumeration of reversible functions and its application to circuit complexity

Giovanni De Micheli, Mathias Soeken, Nabila Abdessaied

We review combinational results to enumerate and classify reversible functions and investigate the application to circuit complexity. In particularly, we consider the effect of negating and permuting input and output variables and the effect of applying li ...

Springer2016

Class number problem

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Algebraic twists of GL(2) automorphic forms

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

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

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

Relax and Recover: Guaranteed Range-Only Continuous Localization

Relax and Recover: Guaranteed Range-Only Continuous Localization

Matrix recovery from bilinear and quadratic measurements

Efficient Verifiable Delay Functions

Quadratic Sieving

Enumeration of reversible functions and its application to circuit complexity

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

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

Relax and Recover: Guaranteed Range-Only Continuous Localization

Algebraic twists of GL(2) automorphic forms

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

Efficient Verifiable Delay Functions

Enumeration of reversible functions and its application to circuit complexity

Relax and Recover: Guaranteed Range-Only Continuous Localization

Matrix recovery from bilinear and quadratic measurements

Quadratic Sieving