scholarly journals Correction to: ``On a positivity property of the Riemann ξ-function'' (Acta Arith. 89 (1999), 217–234)

2005 ◽  
Vol 116 (3) ◽  
pp. 293-294
Author(s):  
Jeffrey C. Lagarias
Keyword(s):  
Acta Arith ◽  
Positivity Property

A POSITIVITY PROPERTY FOR FOLIATIONS ON COMPACT KÄHLER MANIFOLDS

2006 ◽  
Vol 17 (01) ◽  
pp. 35-43 ◽  
Author(s):  
MARCO BRUNELLA
Keyword(s):  
Kähler Manifold ◽  
Rational Curves ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Canonical Bundle ◽  
Positivity Property ◽  
Kahler Manifold ◽  
Compact Kähler Manifold

We prove that the canonical bundle of a foliation by curves on a compact Kähler manifold is pseudoeffective, unless the foliation is a (special) foliation by rational curves.

A positivity property of the Satake isomorphism

2000 ◽  
Vol 101 (2) ◽  
pp. 153-166 ◽  
Author(s):  
Michael Rapoport
Keyword(s):  
Positivity Property ◽  
Satake Isomorphism

SOME REMARKS ON MINIMAL ASYMPTOTIC BASES OF ORDER THREE

2020 ◽  
Vol 102 (1) ◽  
pp. 21-30
Author(s):  
DENGRONG LING ◽  
MIN TANG
Keyword(s):  
Acta Arith ◽  
Powers Of 2

We study a question on minimal asymptotic bases asked by Nathanson [‘Minimal bases and powers of 2’, Acta Arith. 49 (1988), 525–532].

scholarly journals ON A PROBLEM OF BERNIK, KLEINBOCK AND MARGULIS

2011 ◽  
Vol 53 (3) ◽  
pp. 669-681
Author(s):  
NATALIA BUDARINA
Keyword(s):  
Acta Arith ◽  
Algebraic Numbers ◽  
Natural Restriction ◽  
Probabilistic Criterion ◽  
Error Functions ◽  
System Of Inequalities ◽  
Compositio Math ◽  
General Error

AbstractIn this paper, the Khintchine-type theorems of Beresnevich (Acta Arith.90(1999), 97) and Bernik (Acta Arith.53(1989), 17) for polynomials are generalised to incorporate a natural restriction on derivatives. This represents the first attempt to solve a problem posed by Bernik, Kleinbock and Margulis (Int. Math. Res. Notices2001(9) (2001), 453). More specifically, the main result provides a probabilistic criterion for the solvability of the system of inequalities |P(x)| < Ψ1(H) and |P′(x)| < Ψ2(H) in integral polynomialsPof degree ≤nand heightH, where Ψ1and Ψ2are fairly general error functions. The proof builds upon Sprindzuk's method of essential and inessential domains and the recent ideas of Beresnevich, Bernik and Götze (Compositio Math.146(2010), 1165) concerning the distribution of algebraic numbers.

Quasi-uniqueness of the set of "Gaussian prime plus one's"

2014 ◽  
Vol 10 (07) ◽  
pp. 1783-1790
Author(s):  
Jay Mehta ◽  
G. K. Viswanadham
Keyword(s):  
Acta Arith ◽  
Gaussian Integers ◽  
Arithmetical Functions ◽  
Set Of Uniqueness ◽  
Positive Integers ◽  
Complex Valued ◽  
Gaussian Primes

We recall the well-known notion of the set of uniqueness for arithmetical functions, introduced by Kátai and several other mathematicians like Indlekofer, Elliot and Hoffman, independently. We define its analogue for completely additive complex-valued functions over the set of non-zero Gaussian integers with some examples. We show that the set of "Gaussian prime plus one's" along with finitely many Gaussian primes of norm up to some constant K is a set of uniqueness with respect to Gaussian integers. This is analogous to Kátai's result in the case of positive integers [I. Kátai, On sets characterizing number theoretical functions, II, Acta Arith.16 (1968) 1–14].

IN PRAISE OF ORDER UNITS

2012 ◽  
Vol 11 (06) ◽  
pp. 1250120
Author(s):  
DAVID HANDELMAN
Keyword(s):  
Compact Convex ◽  
Convex Polyhedra ◽  
Order Unit ◽  
Positivity Property

We show that the ordered rings naturally associated to compact convex polyhedra with interior satisfy a positivity property known as order unit cancellation, and obtain other general positivity results as well.

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