Related papers: On the large sieve with square moduli
We prove a new Elekes-Szab\'o type estimate on the size of the intersection of a Cartesian product $A\times B\times C$ with an algebraic surface $\{f=0\}$ over the reals. In particular, if $A,B,C$ are sets of $N$ real numbers and $f$ is a…
We derive efficient and reliable goal-oriented error estimations, and devise adaptive mesh procedures for the finite element method that are based on the localization of a posteriori estimates. In our previous work [SIAM J. Sci. Comput.,…
We prove a sharp H\"older estimate for solutions of linear two-dimensional, divergence form elliptic equations with measurable coefficients, such that the matrix of the coefficients is symmetric and has {\em unit determinant}. Our result…
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…
To a finite quadratic module, that is, a finite abelian group D together with a non-singular quadratic form Q:D --> Q/Z, it is possible to associate a representation of either the modular group, SL(2,Z), or its metaplectic cover, Mp(2,Z),…
We study the convergence of these operators in a weighted space of functions on a positive semi-axis and estimate the approximation by using a new type of weighted modulus of continuity and error estimation.
We prove a non-vanishing result of modular L-values with quadratic twists, where the quadratic discriminants are in a short interval. Using this fact and Waldspurger's theorem, we improve the results of Balog-Ono[The chebotarev density…
We show that both primes and smooth numbers are equidistributed in arithmetic progressions to moduli up to $x^{5/8 - o(1)}$, using triply-well-factorable weights for the primes (we also get improvements for the well-factorable linear sieve…
It is well known that the internal suplattices in the topos of sheaves on a locale are precisely the modules on that locale. Using enriched category theory and a lemma on KZ doctrines we prove (the generalization of) this fact in the case…
In 1999 Allan Swett checked (in 150 hours) the Erd\H{o}s-Straus conjecture up to $N=10^{14}$ with a sieve based on a single modular equation. After having proved the existence of a "complete" set of seven modular equations (including three…
Let $\rho$ be a mod $\ell$ Galois representation attached to a newform $f$. Explicit methods are sometimes able to determine the image of $\rho$, or even the number field cut out by $\rho$, provided that $\ell$ and the level $N$ of $f$ are…
In this article, we obtain an explicit version of Heath-Brown's large sieve inequality for quadratic characters and discuss its applications to $L$-functions and quadratic fields.
The Fourier-Mukai transform is lifted to the derived category of sheaves with connection on abelian varieties. The case of flat connections (D-modules) is discussed in detail.
We consider multiplication properties of elements in weighted Fourier Lebesgue and modulation spaces. Especially we extend some results by Pilipovic, Teofanov and Toft (2010).
In this paper we have adapted Bahl and Tuteja (1991) estimator in systematic sampling using auxiliary information. Using Bedi (1996) transformation an improved estimator is also proposed under systematic sampling. The expressions of bias…
We construct symmetric square type $L$-series for vector-valued modular forms transforming under the Weil representation associated to a discriminant form. We study Hecke operators and integral representations to investigate their…
We build on a recent paper on Fourier expansions for the Riemann zeta function. We establish Fourier expansions for certain $L$-functions, and offer series representations involving the Whittaker function $W_{\gamma,\mu}(z)$ for the…
Given a fixed $p\neq 2$, we prove a simple and effective characterization of all radial multipliers of $\cF L^p(\Bbb R^d)$, provided that the dimension $d$ is sufficiently large. The method also yields new $L^q$ space-time regularity…
In this paper, we investigate the large deviations of sums of weighted random variables that are approximately independent, generalizing and improving some of the results of Montgomery and Odlyzko. We are motivated by examples arising from…
We prove an x-ray estimate in general dimension which is stronger than the Kakeya estimates of Wolff. This generalizes an x-ray estimate in three dimensions which is also due to Wolff.