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POSITIVITY OF QCD AT ASYMPTOTIC DENSITY
, 2003
"... In this talk, I try to show that the sign problem of dense QCD is due to modes whose frequency is higher than the chemical potential. An effective theory of quasiquarks near the Fermi surface has a positive measure in the leading order. The higherorder corrections make the measure complex, but they ..."
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, 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.
Asymptotic density and the asymptotics of partition functions ∗
, 2000
"... 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, ..."
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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 problem for upper asymptotic density, The
 Transactions of American Mathematical Society
"... 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 on ..."
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Cited by 11 (8 self)
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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
Asymptotic densities of Maass newforms
 J. Number Theory
"... 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 ..."
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Cited by 3 (0 self)
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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 JacquetLanglands correspondence. Key words: Maass newforms, Weyl law, JacquetLanglands correspondence. 1
Asymptotic Density in Combined Number Systems
"... 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 in the lite ..."
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Cited by 1 (0 self)
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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’s Theorem for Asymptotic Densities
, 2009
"... 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 ab ..."
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Cited by 6 (0 self)
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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
Asymptotic density and the Ershov hierarchy, in preparation
"... 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 nc.e. set if and only if it is a difference of leftΠ02 reals. Further, we show that the densities of th ..."
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Cited by 2 (1 self)
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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 nc.e. set if and only if it is a difference of leftΠ02 reals. Further, we show that the densities
Asymptotic density and computably enumerable sets
"... 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 in ..."
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Cited by 11 (6 self)
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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
Fine asymptotic densities for sets of natural numbers
 Proceedings of the American Mathematical Society
, 2010
"... Abstract. By allowing values in nonArchimedean 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. ..."
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Cited by 1 (0 self)
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Abstract. By allowing values in nonArchimedean 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.
Results 1  10
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4,020