Related papers: On lattices over Fermat function fields
For a real number $x$, call $\frac1n \lfloor nx \rfloor$ the $n$-th lower rational approximation of $x$. We study the functions defined by taking the cumulative average of the first $n$ lower rational approximations of $x$, which we call…
We introduce an alternative stratification of knots: by the size of lattice on which a knot can be first met. Using this classification, we find ratio of unknots and knots with more than 10 minimal crossings inside different lattices and…
It has recently been shown that when $N_f$ generations of chiral fermions are coupled in a specific manner to $N$ (with $N \geq 2N_f-1$) pairs of vectorlike fermions whose mass terms form a one-dimensional lattice-like structure in theory…
We study separation axioms for $X$-top-lattices (i.e. lattices $L$ for which a given subset $X\subseteq L\backslash \{1\}$ admits a \emph{Zariski-like topology}). Such spaces are $T_{0}$ and usually far away from being $T_{2}.$% We give…
The Gilbert type bound for codes in the title is reviewed, both for small and large alphabets. Constructive lower bounds better than these existential bounds are derived from geometric codes, either over Fp or Fp2 ; or over even degree…
Let k be an algebraically closed field of characteristic 0 and let D be a division algebra whose center F contains k. We shall say that D can be reduced to r parameters if D = D_0 tensor_{F_0} F, where D_0 is a division algebra, the center…
We discuss fermions in a spontaneously generated holographic lattice background. The lattice structure at the boundary is generated by introducing a higher-derivative interaction term between a U(1) gauge field and a scalar field. We solve…
There exist numerous results in the literature proving that within certain families of totally real number fields, the minimal rank of a universal quadratic lattice over such a field can be arbitrarily large. Kala introduced a technique of…
Domain-wall fermions preserve chiral symmetry up to terms that decrease exponentially when the lattice size in the fifth dimension is taken to infinity. The associated rates of convergence are given by the low-lying eigenvalues of a simple…
I give an elementary introduction to the study of gauge theories coupled to fermions with many degrees of freedom. Besides their intrinsic interest, these theories are candidates for nonperturbative extensions of the Higgs sector of the…
We study a generalization of the Erd\H{o}s-Falconer distance problem over finite fields. For a graph $G$, two embeddings $p, p': V(G) \to \mathbb{F}_q^d$ of a graph $G$ are congruent if for all edges $(v_i, v_j)$ of $G$ we have that…
Supersymmetry plays prominent roles in the study of quantum field theory and in many proposals for potential new physics beyond the standard model. Lattice field theory provides a non-perturbative regularization suitable for strongly…
We present a natural reverse Minkowski-type inequality for lattices, which gives upper bounds on the number of lattice points in a Euclidean ball in terms of sublattice determinants, and conjecture its optimal form. The conjecture exhibits…
Lattice fermions in a fluctuating gauge field can show localization, much like electrons in a disordered potential. We study the spectrum of localized and extended states of supercritical Wilson fermions in gauge ensembles generated with…
We study the dynamics of SU(2) gauge theory with NF=6 Dirac fermions by means of lattice simulation to investigate if they are appropriate to realization of electroweak symmetry breaking. The discrete analogue of beta function for the…
One important question in the theory of lattices is to detect a shortest vector: given a norm and a lattice, what is the smallest norm attained by a non-zero vector contained in the lattice? We focus on the infinity norm and work with…
We construct a one-parameter family of lattice models starting from a two-dimensional rational conformal field theory on a torus with a regular lattice of holes, each of which is equipped with a conformal boundary condition. The lattice…
The construction of self-dual codes over small fields such that their minimum distances are as large as possible is a long-standing challenging problem in the coding theory. In 2009, a family of binary self-dual cyclic codes with lengths…
Over the last few years lattice techniques have been used to investigate candidate theories of new physics beyond the Standard Model. This review gives a survey of results from these studies. Most of these investigations have been of…
The topological susceptibility is one of the few physical quantities that directly measure the properties of the QCD vacuum. Chiral perturbation theory predicts that in the small quark mass limit the topological susceptibility depends…