Related papers: A Lower Bound for the Large Sieve with Square Modu…

In this paper I prove a conjecture which gives a lower bound for the largest absolute value of the coefficients of the n-th cyclotomic polynomial for some n. Moreover this estimate is essentially sharp.

We give a lower bound for the local height of a non-torsion element of a Drinfeld module.

We give upper bounds on the genus of a curve with general moduli assuming that it can be embedded in a projective nonsingular surface $Y$ so that $\dim(|C|) > 0$. We find such bounds for all types of surfaces of intermediate Kodaira…

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…

Improvements of the Large Sieve for Special Sequences

Sifting limits for the $\Lambda^{2}\Lambda^{-}$ sieve, Selberg's lower bound sieve, are computed for integral dimensions $1<\kappa\le10$. The evidence strongly suggests that for all $\kappa\ge3$ the $\Lambda^{2}\Lambda^{-}$ sieve is…

We describe a semidefinite programming framework for proving upper bounds on concrete sifting problems, and show that the Large Sieve can be interpreted as a special case of this framework. With a small tweak, the Larger Sieve also falls…

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…

We obtain a close to the best possible version of the large sieve inequality with amplitudes given by the values of a polynomial with integer coefficients of degree $\geq 2$.

In this note, we provide a wide range of upper bounds for the moduli of the zeros of a complex polynomial. The obtained bounds complete a series of previous papers on the location of zeros of polynomials.

In this paper we prove parts of a conjecture of Herzog giving lower bounds on the rank of the free modules appearing in the linear strand of a graded $k$-th syzygy module over the polynomial ring. If in addition the module is…

Motivated by asymptotic phenomena of moduli spaces of higher rank stable sheaves on algebraic surfaces, we study the Picard number of the moduli space of one-dimensional stable sheaves supported in a sufficiently positive divisor class on a…

An inequality of Large Sieve type, efficacious in the analytic treatment of Euler products, is obtained.

Many upper bounds for the moduli of polynomial roots have been proposed but reportedly assessed on selected examples or restricted classes only. Regarding quality measured in terms of worst-case relative overestimation of the maximum…

We survey old and new results on the existence of moduli spaces of semistable coherent sheaves both in algebraic and in complex geometry.

We obtain an upper bound for the number of critical points of the systole function on $\mathcal{M}_g$. Besides, we obtain an upper bound for the number of those critical points whose systole is smaller than a constant.

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.

In this paper we establish explicit lower bounds for pseudodifferential operators with a radial symbol. The proofs use classical Weyl calculus techniques and some useful, if not celebrated, properties of the Laguerre polynomials.

We prove the existence of fine moduli spaces of simple coherent sheaves on families of irreducible curves. Our proof is based on the existence of a universal upper bound of the Castelnuovo-Mumford regularity of such sheaves, which we…

Given a closed four-manifold with $b_1=0$ and a prime number $p$, we prove that for any mod $p^r$ basic class, the virtual dimension of the Seiberg-Witten moduli space is bounded above by $2r(p-1)-2$ under some conditions on $r$ and…