Related papers: Bounds on the Hilbert-Kunz Multiplicity
We treat the boundary problem for complex varieties with isolated singularities, of complex dimension greater than or equal to 3, non necessarily compact, which are contained in strongly convex, open subsets of a complex Hilbert space H. We…
The Hilbert-Kunz multiplicity and $F$-signature are important invariants for researchers in commutative algebra and algebraic geometry. We provide software, and describe the automation of a calculation, for the two invariants in the case of…
We study the bounded negativity conjecture for non-quaternionic Hilbert modular surfaces and give an explicit bound for the special case of Hirzebruch-Zagier curves on Hilbert modular surfaces.
We give one sufficient and two necessary conditions for boundedness between Lebesgue or Lorentz spaces of several classes of bilinear multiplier operators closely connected with the bilinear Hilbert transform.
We show that the biharmonic Hilbert complex with mixed boundary conditions on bounded strong Lipschitz domains is closed and compact. The crucial results are compact embeddings which follow by abstract arguments using functional analysis…
In this paper, we present several new bounds for the norm and numerical radius of sums of Hilbert space operators. The obtained bounds form a new collection that enriches our understanding of these bounds. We compare our bounds with the…
The aim of this manuscript is to discuss the Hilbert-Kunz functions over an excellent local ring regular in codimension one. We study the shape of the Hilbert-Kunz functions of modules and discuss the properties of the coefficient of the…
In the present paper we establish the solvability of the Regularity boundary value problem in domains with (flat and Lipschitz) lower dimensional boundaries for operators whose coefficients exhibit small oscillations analogous to the…
In this work we provide an upper bound for the multiplicity of a one-dimensional Cohen-Macaulay ring (under certain conditions), describe the rings attaining the equality for this bound, and outline a connection with Wilf's conjecture for…
We obtain upper bounds on the cardinality of Hilbert cubes in finite fields, which avoid large product sets and reciprocals of sum sets. In particular, our results replace recent estimates of N. Hegyv\'ari and P. P. Pach (2020), which…
We establish new upper bounds for the numerical radius of bounded linear operators on a complex Hilbert space by introducing weighted geometric means of the modulus of an operator and its adjoint. This approach yields a family of…
In this paper, we introduce new general frameworks for estimating the maximal dimension of Hilbert cubes contained in finite truncations of arbitrary sets. As applications, we investigate Hilbert cubes in a range of arithmetic sets,…
New upper and lower bounds on the Castelnuovo-Mumford regularity are given in terms of the Hilbert coefficients. Examples are provided to show that these bounds are in some sense nearly sharp.
We consider an elliptic problem with unknowns on the boundary of the domain of the elliptic equation and suppose that the right-hand side of this equation is square integrable and that the boundary data are arbitrary (specifically,…
Let S be a finitely generated standard multi-graded algebra over a Noetherian local ring A. This paper first expresses mixed multiplicities of S in term of Hilbert-Samuel multiplicity that explained the mixed multiplicities S as the…
Let $R$ be an excellent Noetherian ring of prime characteristic. Consider an arbitrary nested pair of ideals (or more generally, a nested pair of submodules of a fixed finite module). We do \emph{not} assume that their quotient has finite…
We show that the de Rham Hilbert complex with mixed boundary conditions on bounded strong Lipschitz domains is closed and compact. The crucial results are compact embeddings which follow by abstract arguments using functional analysis…
We give lower and upper bounds on the Buchsbaum-Rim multiplicity of finitely generated torsion-free modules over two-dimensional regular local rings, and conditions for them to attain the bounds. As consequences, we have formulae on the…
The main goal of this paper is to present new bounds for certain inner products in Hilbert spaces, with applications to the numerical radius and the operator norm. The obtained results significantly improve earlier results in this…
We show that the Hilbert-Kunz multiplicities of the reductions to positive characteristics of an irreducible projective curve in characteristic 0 have a well-defined limit as the characteristic tends to infinity.