Related papers: Computing quadratic function fields with high 3-ra…
In this paper, we study simple cubic fields in the function field setting, and also generalize the notion of a set of exceptional units to cubic function fields, namely the notion of $k$-exceptional units. We give a simple proof that the…
In this paper we define a pair of faithful functors that map isomorphic and isotopic finite-dimensional algebras over finite fields to isomorphic graphs. These functors reduce the cost of computation that is usually required to determine…
We prove the existence of infinitely many real and imaginary fields whose 5-rank of the class group is >=3.
We give new explicit constructions of several fundamental objects in linear-algebraic pseudorandomness and combinatorics, including lossless rank extractors, weak subspace designs, and strong $s$-blocking sets over finite fields. Our focus…
We consider the problem of approximating partition functions for Ising models. We make use of recent tools in combinatorial optimization: the Sherali-Adams and Lasserre convex programming hierarchies, in combination with variational methods…
We extend to characteristic two recent results about isotropy of quadratic forms over function fields. In particular, we provide a characterization of function fields not only of quadratic forms but also more generally of polynomials in…
We prove that any function with real-valued coefficients, whose input is 4 binary variables and whose output is a real number, is perfectly equivalent to a quadratic function whose input is 5 binary variables and is minimized over the new…
Motivated by a use case in theoretical hadron physics, we revisit an application of a pole-sum fit to dressing functions of a confined quark propagator. More precisely, we investigate approaches to determine the number and positions of the…
In this paper, we obtain an asymptotic formula for the number of imaginary quadratic fields with prime discriminant and class number up to $H$, as $H\to \infty$. Previously, such an asymptotic was only known under the assumption of the…
We present an overview of the existing methods for computing functional determinants, and outline a possible way forward for Hamiltonians of higher dimensions without radial symmetry.
We prove a function field analogue of Maynard's result about primes with restricted digits. That is, for certain ranges of parameters n and q, we prove an asymptotic formula for the number of irreducible polynomials of degree n over a…
We count algebraic points of bounded height and degree on the graphs of certain functions analytic on the unit disk, obtaining a bound which is polynomial in the degree and in the logarithm of the multiplicative height. We combine this work…
Functional determinants of differential operators play a prominent role in theoretical and mathematical physics, and in particular in quantum field theory. They are, however, difficult to compute in non-trivial cases. For one dimensional…
We determine an explicit triangular integral basis for any separable cubic extension of a rational function field over a finite field in any characteristic. We obtain a formula for the discriminant of every such extension in terms of a…
The authors' previous results on the arity gap of functions of several variables are refined by considering polynomial functions over arbitrary fields. We explicitly describe the polynomial functions with arity gap at least 3, as well as…
We design new approximation algorithms for the Multiway Cut problem, improving the previously known factor of 1.32388 [Buchbinder et al., 2013]. We proceed in three steps. First, we analyze the rounding scheme of Buchbinder et al., 2013 and…
We show that spin systems with bounded degrees and coupling independence admit fully polynomial time approximation schemes (FPTAS). We design a new recursive deterministic counting algorithm to achieve this. As applications, we give the…
A triangular field of rational numbers is characterized, with relations to Stirling numbers 2nd, Hyperbolic functions, and centered Binomial distribution. A Generating function is given.
The main outcomes of the paper are divided into two parts. First, we present a new dual for quadratic programs, in which, the dual variables are affine functions, and we prove strong duality. Since the new dual is intractable, we consider a…
This note provides new methods for constructing quadratic nonresidues in finite fields of characteristic p. It will be shown that there is an effective deterministic polynomial time algorithm for constructing quadratic nonresidues in finite…