Related papers: On Baker type lower bounds for linear forms
We obtain optimal lower bounds for moments of theta functions. On the other hand, we also get new upper bounds on individual theta values and moments of theta functions on average over primes. The upper bounds are based on bounds of…
We give a generalization of Kung's theorem on critical exponents of linear codes over a finite field, in terms of sums of extended weight polynomials of linear codes. For all i=k+1,...,n, we give an upper bound on the smallest integer m…
The Lie algebra of planar vector fields with coefficients from the field of rational functions over an algebraically closed field of characteristic zero is considered. We find all finite-dimensional Lie algebras that can be realized as…
We study degree bounds on rational but not necessarily polynomial generators for the field $\mathbf{k}(V)^G$ of rational invariants of a linear action of a finite abelian group. We show that lattice-theoretic methods used recently by the…
Recent theorems of Dubickas and Mossinghoff use auxiliary polynomials to give lower bounds on the Weil height of an algebraic number $\alpha$ under certain assumptions on $\alpha$. We prove a theorem which introduces an auxiliary polynomial…
Many statistical applications require establishing central limit theorems for sums, integrals, or for quadratic forms of functions of a stationary process. A particularly important case is that of Appell polynomials, since the Appell…
We apply polynomial techniques (linear programming) to obtain lower and upper bounds on the covering radius of spherical designs as function of their dimension, strength, and cardinality. In terms of inner products we improve the lower…
In this article, the standard correspondence between the ideal class group of a quadratic number field and the equivalence classes of binary quadratic forms of given discriminant is generalized to any base number field of narrow class…
In this article, We introduce a condition that is both necessary and sufficient for a linear code to achieve minimality when analyzed over the rings $\mathbb{Z}_{n}$.The fundamental inquiry in minimal linear codes is the existence of a…
This paper continues the investigation begun in arXiv:1906.05602 of extending the T1 theorem of David and Journ\'e, and optimal cancellation conditions, to more general weight pairs. The main additional tool developed here is a two weight…
We first extend the multiplicativity property of arithmetic functions to the setting of operators on the Fock space. Secondly, we use phase operators to get representation of some extended arithmetic functions by operators on the Hardy…
For certain real quadratic fields $K$ with sufficiently small discriminant we produce explicit unit generators for specific ray class fields of $K$ using a numerical method that arose in the study of complete sets of equiangular lines in…
Given a primitive collection of vectors in the integer lattice, we count the number of ways it can be extended to a basis by vectors with sup-norm bounded by $T$, producing an asymptotic estimate as $T \to \infty$. This problem can be…
The problem of simultaneous decomposition of binary forms as sums of powers of linear forms is studied. For generic forms the minimal number of linear forms needed is found and the space parametrizing all the possible decompositions is…
We estimate, in a number field, the number of elements and the maximal number of linearly independent elements, with prescribed bounds on their valuations. As a by-product, we obtain new bounds for the successive minima of ideal lattices.…
System of alternatively orthogonalized rational functions of Jacobi type on the half line $[1, \infty)$ is defined and its properties are established. Three subsystems of proper and mixed systems of rational functions with nice properties…
Let $S=\mathbb{K}[x_1,\ldots,x_n]$ the polynomial ring over a field $\mathbb{K}$. In this paper for some families of monomial ideals $I \subset S$ we study the minimal number of generators of $I^k$. We use this results to find some other…
This paper studies two topics concerning on the orthogonal complement of one dimensional subspace with respect to a given quadratic form on a vector space over a number field. One is to determine the invariants for the isomorphism class of…
We revisit, with a pedagogical heuristic motivation, the lambda extension of the low-temperature row correlation functions C(M,N) of the two-dimensional Ising model. In particular, using these one-parameter series to understand the…
We characterize componentwise linear monomial ideals with minimal Taylor resolution and consider the lower bound for the Betti numbers of componentwise linear ideals.