Related papers: The large sieve with square norm moduli in Z[i]

Let $K$ be a global field and let $Z$ be a geometrically irreducible algebraic variety defined over $K$. We show that if a big set $S\subseteq Z$ of rational points of bounded height occupies few residue classes modulo $\mathfrak{p}$ for…

In this paper we study deformation classes of moduli spaces of sheaves on a projective K3 surface. More precisely, let $(S1,H1)$ and $(S2,H2)$ be two polarized K3 surfaces, $m\in\mathbb{N}$, and for $i=1,2$ let $mv_{i}$ be a Mukai vector on…

We prove an inequality for unitarily invariant norms that interpolates between the Arithmetic-Geometric Mean inequality and the Cauchy-Schwarz inequality.

We consider the partition function Z(N;x_1,...,x_N,y_1,...,y_N) of the square ice model with domain wall boundary. We give a simple proof of the symmetry of Z with respect to all its variables when the global parameter a of the model is set…

We describe a very general abstract form of sieve based on a large sieve inequality which generalizes both the classical sieve inequality of Montgomery (and its higher-dimensional variants), and our recent sieve for Frobenius over function…

We obtain some inequalities which are stronger than the Schur majorization inequalities.

We obtain some new inequalities of Chebyshev Type.

We construct new examples of cubic surfaces, for which the Hasse principle fails. Thereby, we show that, over every number field, the counterexamples to the Hasse principle are Zariski dense in the moduli scheme of non-singular cubic…

In this note we are concerned about the generalization of the GHS inequality for the Potts model. We also obtain by a different method the proof of the GHS inequality for the Ising model. We take advantage of a polynomial expansion and we…

We prove new bounds for weighted mean values of sums involving Fourier coefficients of cusp forms that are automorphic with respect to a Hecke congruence subgroup \Gamma =\Gamma_0(q) of the group SL(2,Z[i]), and correspond to exceptional…

We prove a result on the distribution of the general divisor functions in arithmetic progressions to smooth moduli which exceed the square root of the length.

In this paper, we study the uniform and couniform dimensions of inverse polynomial modules over skew Ore polynomials.

We give a simple proof of a recently result concerning Hardy $q$-inequalities.

This is a survey paper discussing the moduli problem for varieties of general type.

We prove $p$-adic uniformization for Shimura curves attached to the group of unitary similitudes of certain binary skew hermitian spaces $V$ with respect to an arbitrary CM field $K$ with maximal totally real subfield $F$. For a place $v|p$…

We prove an extension of the Bourgain-Sarnak-Ziegler theorem and then apply it to bound certain polynomial exponential sums with modular coefficients.

In this note we prove a weighted version of the Khintchine inequalities.

Recently proved weighted Cauchy Scwarz inequality for Hilbert $C^*$-modules leads to many H\"older type inequalities for unitarily invariant norms on Hilbert space operators.

In this note we compute length, support and dimension of syzygy modules of certain modules. This partially answers questions asked by Huneke et al.

Given a smooth, complete Riemannian manifold $M$ with bounded Ricci curvature and positive injectivity radius, we derive a sharp Sobolev inequality for the embedding of $W^{1,p}(M)$ into $L^{\frac{np}{n-p}}(M)$, when $1\le p< n$. We will…