Publications related to Quadratic Sieving

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Nonlinear optical frequency conversion is of fundamental importance in photonics and underpins countless of its applications: Sum- and difference-frequency generation in media with quadratic nonlinearity permits reaching otherwise inaccessible wavelength r ...

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 ...

In materials, certain approximated symmetry operations can exist in a lower-order approximation of the effective model but are good enough to influence the physical responses of the system, and these approximated symmetries were recently dubbed "quasisymme ...

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 ...

We consider fundamental algorithmic number theoretic problems and their relation to a class of block structured Integer Linear Programs (ILPs) called 2-stage stochastic. A 2-stage stochastic ILP is an integer program of the form min{c(T)x vertical bar Ax = ...

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 ...

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 ...

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 ...

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 ...

We introduce a residual-based a posteriori error estimator for contact problems in two- and three-dimensional linear elasticity, discretized with linear and quadratic finite elements and Nitsche’s method. Efficiency and reliability of the estimator are pro ...

We apply a Gaussian variational approximation to model reduction in large biochemical networks of unary and binary reactions. We focus on a small subset of variables (subnetwork) of interest, e.g. because they are accessible experimentally, embedded in a l ...

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 ...

In the context of static real-time optimization (RTO) of uncertain plants, the standard modifier-adaptation scheme consists in adding first-order correction terms to the cost and constraint functions of a model based optimization problem. If the algorithm ...

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 ...

We introduce a novel class of term structure models for variance swaps. The multivariate state process is characterized by a quadratic diffusion function. The variance swap curve is quadratic in the state variable and available in closed form, greatly faci ...

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 ...

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 ...

RATIONALE: Previously described methods for producing absorption mode Fourier transform ion cyclotron resonance (FTICR) mass spectra have all relied on the phase correction function being quadratic. This assumption has been found to be invalid for some ins ...

We derive a Motohashi-type formula for the cubic moment of central values of -functions of level cusp forms twisted by quadratic characters of conductor , previously studied by Conrey and Iwaniec and Young. Corollaries of this formula include Weyl-subconve ...

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. ...

Quadratic Sieving

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Simulating supercontinua from mixed and cascaded nonlinearities

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

Hierarchy of quasisymmetries and degeneracies in the CoSi family of chiral crystal materials

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

The double exponential runtime is tight for 2-stage stochastic ILPs

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

Relax and Recover: Guaranteed Range-Only Continuous Localization

Petersson inner products of weight-one modular forms

Efficient Verifiable Delay Functions

Residual-based a posteriori error estimation for contact problems approximated by Nitsche's method

Statistical physics approaches to subnetwork dynamics in biochemical systems

Bilinear forms with Kloosterman sums and applications

A feasible-side globally convergent modifier-adaptation scheme

Enumeration of reversible functions and its application to circuit complexity

Quadratic variance swap models

Computational Aspects of Jacobians of Hyperelliptic Curves

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

Producing absorption mode Fourier transform ion cyclotron resonance mass spectra with non-quadratic phase correction functions

A twisted Motohashi formula and Weyl-subconvexity for -functions of weight two cusp forms

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