, but they are suppressed as long as the chemical potential is sufficiently larger than ΛQCD. As a consequence of the positivity of the effective theory, we can show that the global vector symmetries except the U(1) baryon number are unbroken at asymptotic density. 1.

Let A be a set of positive integers with gcd(A) = 1, and let pA(n) be the partition function of A. Let c0 = π √ 2/3. If A has lower asymptotic density α and upper asymptotic density β, then lim inf log pAn/c0 n ≥ α and lim sup log pA(n)/c0 n ≤ β. In particular, if A has asymptotic density α> 0

Inverse problems study the structure of a set A when the “size ” of A + A is small. In the article, the structure of an infinite set A of natural numbers with positive upper asymptotic density is characterized when A is not a subset of an infinite arithmetic progression of difference greater than

We define the counting function for Maass newforms of Hecke congruence groups and calculate the three main terms of this counting function. We then give necessary and sufficient conditions for this expansion to have the same shape as if it were counting eigenvalues related to cocompact surfaces. We relate the result to classical instances of the Jacquet-Langlands correspondence. Key words: Maass newforms, Weyl law, Jacquet-Langlands correspondence. 1

Abstract not found

Abstract. Necessary and sufficient conditions are found for a combination of additive number systems and a combination of multiplicative number systems to preserve the property that all partition sets have asymptotic density. These results cover and extend several special cases mentioned

Plünnecke proved that if B ⊆ N is a basis of order h> 1, i.e., σ(hB) = 1, then σ(A+B)> σ(A)1 − 1h where A is an arbitrary subset of N and σ represents Shnirel’man density. In this paper we explore whether σ can be replaced by other asymptotic densities. We show that Plünnecke’s inequality

Abstract. We classify the asymptotic densities of the ∆02 sets according to their level in the Ershov hierarchy. In particular, it is shown that for n ≥ 2, a real r ∈ [0, 1] is the density of an n-c.e. set if and only if it is a difference of left-Π02 reals. Further, we show that the densities

We study connections between classical asymptotic density, computability and computable enumerability. In an earlier paper, the second two authors proved that there is a computably enumerable set A of density 1 with no computable subset of density 1. In the current paper, we extend this result

Abstract. By allowing values in non-Archimedean extensions of the unit interval, we consider finitely additive measures that generalize the asymptotic density. The existence of a natural class of such “fine densities ” is independent of ZFC.