Related papers: The large sieve inequality with square moduli for …

We prove a Hardy inequality for ultraspherical expansions by using a proper ground state representation. From this result we deduce some uncertainty principles for this kind of expansions. Our result also implies a Hardy inequality on…

This paper is the sequel of the paper "Continuity of volumes on arithmetic varieties", in which we established the arithmetic volume function of smooth hermitian Q-invertible sheaves and proved its continuity. The continuity of the volume…

This paper presents an adaptation of recently developed algorithms for quadratic forms over number fields in arXiv:1304.0708 to global function fields of odd characteristics. First, we present algorithm for checking if a given…

In this paper we obtain a sharp upper bound for the number of solutions to a certain diophantine inequality involving fractions with power denominator. This problem is motivated by a conjecture of Zhao concerning the spacing of such…

In this paper we give construct good moduli spaces for constructible sheaves and Stokes functors. Derived enhancement of such are also considered.

We study large values of quadratic character sums with summation lengths exceeding the square root of the modulus. Assuming the Generalized Riemann Hypothesis, we obtain a new Omega result.

In this article we study the fields generated by the Fourier coefficients of modular forms at arbitrary cusps. We prove that these fields are contained in certain cyclotomic extensions of the field generated by the Fourier coefficients at…

We provide new necessary and sufficient conditons for ensuring strong quasiconvexity in the nonsmooth case and, as a consequence, we provide a proof for the differentiable case. Furthermore, we improve the quadratic growth property for…

In this short article we generalize the Sobolev's inequalities for the module of continuity for the functions belonging to the classical Lebesgue space on the (Bilateral) Grand Lebesgue spaces. We construct also some examples in order to…

50 years after Thompson's famous triangle inequality for the operator right modulus, we establish a triangle inequality for the quadratic symmetric modulus. We also discuss the corresponding equality cases as well as the…

In the paper, the authors introduce a new concept "extended $s$-convex functions", establish some new integral inequalities of Hermite-Hadamard type for this kind of functions, and apply these inequalities to derive some inequalities of…

We prove an exponential integral estimate for the quadratic partial sums of multiple Fourier series on large sets that implies some new properties of Fourier series.

We extend to characteristic two recent results about isotropy of quadratic forms over function fields. In particular, we provide a characterization of function fields not only of quadratic forms but also more generally of polynomials in…

In this paper we show how the superquadratic functions can be used as a tool for researching other types of convex functions like $\phi $-convexity, strong-convexity and uniform convexity. We show how to use inequalities satisfied by…

In the prequel to this paper, two versions of Le Potier's strange duality conjecture for sheaves over abelian surfaces were studied. A third version is considered here. In the current setup, the isomorphism involves moduli spaces of sheaves…

We formulate for function fields an analog of Serre's conjecture on the modularity of 2-dimensional irreducible mod l representations of the absolute Galois group of Q: our analog is not restricted to 2-dimensional represntations. While the…

The size function for a number field is an analogue of the dimension of the Riemann-Roch spaces of divisors on an algebraic curve. It was conjectured to attain its maximum at the trivial class of Arakelov divisors. This conjecture was…

We combine Hooley neutralisers and the large sieve for quadratic characters. We give applications to character sums with a hyperbolic height condition.

We survey recent advances in the theory of moduli spaces of stable sheaves on hyperk\"ahler manifolds of dimension greater than $2$. We start by recalling the well-known theory in dimension $2$, i.e.~for $K3$ surfaces, emphasizing the…

We generalise remarks of Euler and of Perron by explaining how to detail all quadratic irrational integers for which the symmetric part of the period of their continued fraction expansion commences with prescribed partial quotients. The…