Sign changes of Δ(1)(x)

2021 ◽  
Author(s):  
Dan Liu ◽  
Yankun Sui
Keyword(s):  
Sign Changes

scholarly journals Sign changes in the prime number theorem

2021 ◽  
Author(s):  
Thomas Morrill ◽  
Dave Platt ◽  
Tim Trudgian
Keyword(s):  
Prime Number ◽  
Prime Number Theorem ◽  
Sign Changes

scholarly journals Ordering risk bounds in factor models

2018 ◽  
Vol 6 (1) ◽  
pp. 259-287 ◽  
Author(s):  
Jonathan Ansari ◽  
Ludger Rüschendorf
Keyword(s):  
Risk Factor ◽  
Systemic Risk ◽  
Factor Models ◽  
Worst Case ◽  
Sign Changes ◽  
Risk Factor Models ◽  
Risk Bounds ◽  
Derivatives Of ◽  
Dependence Structures

AbstractConditionally comonotonic risk vectors have been proved in [4] to yield worst case dependence structures maximizing the risk of the portfolio sum in partially specified risk factor models. In this paper we investigate the question how risk bounds depend on the specification of the pairwise copulas of the risk components Xiwith the systemic risk factor. As basic toolwe introduce a new ordering based on sign changes of the derivatives of copulas. This together with discretization by n-grids and the theory of supermodular transfers allows us to derive concrete ordering criteria for the maximal risks.

Sign changes of Fourier coefficients of cusp forms supported on prime power indices

2014 ◽  
Vol 10 (08) ◽  
pp. 1921-1927 ◽  
Author(s):  
Winfried Kohnen ◽  
Yves Martin
Keyword(s):  
Positive Integer ◽  
Prime Power ◽  
Fourier Coefficients ◽  
Cusp Forms ◽  
Power Indices ◽  
Hecke Operator ◽  
Sign Changes ◽  
Integral Weight ◽  
Hecke Eigenform ◽  
Almost All

Let f be an even integral weight, normalized, cuspidal Hecke eigenform over SL2(ℤ) with Fourier coefficients a(n). Let j be a positive integer. We prove that for almost all primes p the sequence (a(pjn))n≥0 has infinitely many sign changes. We also obtain a similar result for any cusp form with real Fourier coefficients that provide the characteristic polynomial of some generalized Hecke operator is irreducible over ℚ.

Next-To-Interpolatory Approximation on Sets with Multiplicities

1966 ◽  
Vol 18 ◽  
pp. 1196-1211 ◽  
Author(s):  
T. S. Motzkin ◽  
A. Sharma
Keyword(s):  
Real Numbers ◽  
Sign Changes ◽  
Positive Weights ◽  
The Difference ◽  
Unique Polynomial

It is known that given a set X of m (⩾n) distinct real numbers and a real-valued function f denned on X, there exists a unique polynomial pn-1,f,x of degree n — 1 or less which approximates best to f(x) on X, that is, which minimizes the deviation δ = δ(f, p) defined by the αth-power metric (α < 1) with positive weights, or by the positively weighted maximum of |f — p| on X; these deviations shall be denoted by δα and δβ. The polynomial pn-1,f,x has the property that f — pn-1,f,x has at least n strong sign changes; in other words, there are at least n + 1 points in X where the difference takes alternatingly positive and negative values.

scholarly journals Dispersive ordering results

1983 ◽  
Vol 15 (04) ◽  
pp. 889-891 ◽  
Author(s):  
James Lynch ◽  
Gillian Mimmack ◽  
Frank Proschan
Keyword(s):  
Simple Proof ◽  
Total Positivity ◽  
Sign Changes ◽  
Dispersive Ordering

A distribution F is less dispersed than a distribution G if for all . We generalize a characterization of dispersive ordering of Shaked (1982) concerning sign changes of Fc – G, where Fc is a translate of F. We then use this generalization plus total positivity to develop a simple proof of a characterization of dispersive distributions due to Lewis and Thompson (1981); a distribution H is dispersive if

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