Density of solutions to quadratic congruences

A classical result in number theory is Dirichlet's theorem on the density of primes in an arithmetic progression. We prove a similar result for numbers with exactly k prime factors for k>1. Building upon a proof by E.M. Wright in 1954, we compute the natural density of such numbers where each prime satisfies a congruence condition. As an application, we obtain the density of squarefree n not greater than x with k prime factors such that a fixed quadratic equation has exactly 2^k solutions modulo n

Study of hyperon-hyperon correlations and search for HH-dibaryon using STAR detector at RHIC

High yield of strange particle production per central collision in nucleus-nucleus collisions at RHIC and high statistics data set from STAR experiment allow us to measure \Lambda\Lambda correlations. The \Lambda\Lambda correlation measurement is also closely related to a possible six-quark state H-dibaryon, which is yet to be observed experimentally. The first measurement of \Lambda\Lambda correlations in Au+Au collisions for \sqrt{s_{NN}}= 39, 62.4 and 200 GeV and search for H-dibaryon with its weak decay \Lambda p\pi in Au+Au collisions for \sqrt{s_{NN}}= 200 GeV using the STAR experiment at RHIC are presented here.Comment: conference proceedings for Strangeness in Quark Matter 2011, Cracow, Poland, September 18-24, 201