Related papers: On Baker type lower bounds for linear forms
We study lower bounds for the norm of the product of polynomials and their applications to the so called \emph{plank problem.} We are particularly interested in polynomials on finite dimensional Banach spaces, in which case our results…
We compare the level zero part of the type of a representation of GL(n) over a non-archimedean local field with the tame part of its Langlands parameter restricted to inertia. By normalizing this comparison, we construct canonical…
We provide a variant of Baer's theorem about isomorphism of endomorphism rings of vector spaces over division rings, where the full endomorphism rings are replaced by some subrings of finitary maps.
We develop a purely combinatorial theory of limit linear series on metric graphs. This will be based on the formalisms of hypercube rank functions and slope structures. We provide a full classification of combinatorial limit linear series…
Algebraic surfaces in the complex projective space with a high number of A-type singularities have been presented in a recent paper. We extend the construction in order to obtain lower bounds for the maximal number of A singularities for…
In these lectures we give an introduction to the reduction theory of binary forms starting with quadratic forms with real coefficients, Hermitian forms, and then define the Julia quadratic for any degree $n$ binary form. A survey of a…
We study some properties of quadratic forms with values in a field whose underlying vector spaces are endowed with the structure of right vector spaces over a division ring extension of that field. Some generalized notions of isotropy,…
The local minima of a quadratic functional depending on binary variables are discussed. An arbitrary connection matrix can be presented in the form of quasi-Hebbian expansion where each pattern is supplied with its own individual weight.…
Work in progress concerning alternative formalizations of arithmetic.
In this note we consider weighted conditional type operators between different Orlicz spaces and generalized conditional type Holder inequality that we defined in [2]. Then we give some necessary and sufficient conditions for boundedness of…
We give upper bounds on the size of the gap between a non-zero constant term and the next non-zero Fourier coefficient of an entire level two modular form. We give upper bounds for the minimum positive integer represented by a level two…
Problems in additive number theory related to sum and difference sets, more general binary linear forms, and representation functions of additive bases for the integers and nonnegative integers.
Basic elements of integral calculus over algebras of iterated differential forms, are presented. In particular, defining complexes for modules of integral forms are described and the corresponding berezinians and complexes of integral forms…
This article handles in a short manner a few Laplace transform pairs and some extensions to the basic equations are developed. They can be applied to a wide variety of functions in order to find the Laplace transform or its inverse when…
In this article we give an analogue of Hecke and Sturm bounds for Hilbert modular forms over real quadratic fields. Let $K$ be a real quadratic field and $\Om_K$ its ring of integers. Let $\Gamma$ be a congruence subgroup of $\SL_2(\Om_K)$…
In this paper, we study the diagonal restrictions of certain Hilbert theta series for a totally real field $F$, and prove that they span the corresponding space of elliptic modular forms when the $F$ is quadratic or cubic. Furthermore, we…
New lower bounds involving sum, difference, product, and ratio sets for $A\subset \C$ are given.
Abstrct: In this note, by considering fractionally linear functions over a finite field and consequently developing an abstract sequence, we study some of its properties.
Let $k_i\ (i=1,2,\ldots,t)$ be natural numbers with $k_1>k_2>\cdots>k_t>0$, $k_1\geq 2$ and $t<k_1.$ Given real numbers $\alpha_{ji}\ (1\leq j\leq t,\ 1\leq i\leq s)$, we consider polynomials of the shape…
In this paper we prove a new Myers' type diameter estimate on a complete connected Reimannian manifold which admits a bounded vector field such that the Bakry-\'Emery Ricci tensor has a positive lower bound. The result is sharper than…