Bounds for the Euclidean minima of function fields

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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 ...

Let K be a totally real number field of degree n >= 2. The inverse different of K gives rise to a lattice in Rn. We prove that the space of Schwartz Fourier eigenfunctions on R-n which vanish on the "component-wise square root" of this lattice, is infinite ...

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 ...

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 ...

In the last decade, Ultra High Performance Fibre Reinforced cement-based Composites (UHPFRC) have been increasingly implemented for rehabilitation and strengthening purposes, rendering outstanding results. The ease of application, along with their superior ...

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 ([ ...

Embeddings of maximal tori in classical groups over fields of characteristic not 2 are the subject matter of several recent papers. The aim of the present paper is to give necessary and sufficient conditions for such an embedding to exist, when the base fi ...

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 ...

The Grid Explicit Congestion Notification control mechanism (GECN) is a broadcast-based real-time demand- response mechanism designed for primary voltage control in Active Distribution Networks (ADNs) [1,2]. An extensive set of off-line simulations has ind ...

This work generalizes the one-step model previously developed on fcc-bcc martensitic transformations to the larger family of phase transitions in the fcc-bcc-hcp system. The angular distortive matrices are calculated for the bcc-fcc, bcc-hcp and fcc-hcp tr ...

We show that the transcendence degree of a real function field over an arbitrary real base field is a strict lower bound for its Pythagoras number and a weak lower bound for all its higher Pythagoras numbers. ...

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 ...

A recently found local-global principle for quadratic forms over function fields of curves over a complete discretely valued field is applied to the study of quadratic forms, sums of squares, and related field invariants. ...

Let be a symmetric space of noncompact type. A result of Gelander provides exponential upper bounds in terms of the volume for the torsion homology of the noncompact arithmetic locally symmetric spaces . We show that under suitable assumptions on this resu ...

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 ...

The aim of this paper is to give new upper bounds for Euclidean minima of algebraic number fields. In particular, to show that Minkowski's conjecture holds for the maximal totally real subfields of cyclotomic fields of prime power conductor. ...

This thesis deals with the study of ideal lattices over number fields. Let K be a number field, which is assumed to be CM or totally real. An ideal lattice over K is a pair (I,b), where I is a fractional ideal of K and b : I × I → R is a symmetric positive ...

This work is dedicated to developing algebraic methods for channel coding. Its goal is to show that in different contexts, namely single-antenna Rayleigh fading channels, coherent and non-coherent MIMO channels, algebraic techniques can provide useful tool ...

The performance of HTS devices is strongly influenced by local values of the current/field distributions. In this paper, we investigate the influence of the magnetic field and of the geometrical configuration on the loss behaviour of a 200kVA FCL prototype ...

Bounds for the Euclidean minima of function fields

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Algebraic twists of GL(2) automorphic forms

Fourier non-uniqueness sets from totally real number fields

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

Efficient Verifiable Delay Functions

Towards the use of UHPFRC in railway bridges: the rehabilitation of Buna Bridge

Inhomogeneous minima of mixed signature lattices

Embeddings of maximal tori in classical groups over local and global fields

Computational Aspects of Jacobians of Hyperelliptic Curves

Hardware-in-the-loop Validation of the Grid Explicit Congestion Notification Mechanism for Primary Voltage Control in Active Distribution Networks

Angular distortive matrices of phase transitions in the fcc-bcc-hcp system

Lower bounds for Pythagoras numbers of function fields

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

Sums Of Squares In Algebraic Function Fields Over A Complete Discretely Valued Field

Torsion homology of arithmetic lattices and K-2 of imaginary fields

Algebraic Divisibility Sequences Over Function Fields

Upper bounds for Euclidean minima of algebraic number fields

Réseaux idéaux sur des corps CM et des corps totalement réels

Algebraic methods for channel coding

Analysis of magnetic field and geometry effects in the design of HTS devices for AC power applications