ELLIPTIC CURVES AND -ADIC ELLIPTIC TRANSCENDENCE

2021 ◽  
pp. 1-6
Author(s):  
DUC HIEP PHAM
Keyword(s):  
Elliptic Curves ◽  
Short Proof ◽  
Linear Independence ◽  
Elliptic Functions ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Algebraic Numbers ◽  
Algebraic Dependence ◽  
Necessary And Sufficient

Abstract We prove a necessary and sufficient condition for isogenous elliptic curves based on the algebraic dependence of p-adic elliptic functions. As a consequence, we give a short proof of the p-adic analogue of Schneider’s theorem on the linear independence of p-adic elliptic logarithms of algebraic points on two nonisogenous elliptic curves defined over the field of algebraic numbers.

scholarly journals On The Convolution of a Box Spline With a Compactly Supported Distribution: Linear Independence for the Integer Translates

1991 ◽  
Vol 43 (1) ◽  
pp. 19-33 ◽  
Author(s):  
Charles K. Chui ◽  
Amos Ron
Keyword(s):  
Laplace Transform ◽  
Critical Points ◽  
Linear Independence ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Compactly Supported ◽  
Integer Translates ◽  
Box Spline ◽  
Finite Set ◽  
Necessary And Sufficient

AbstractThe problem of linear independence of the integer translates of μ * B, where μ is a compactly supported distribution and B is an exponential box spline, is considered in this paper. The main result relates the linear independence issue with the distribution of the zeros of the Fourier-Laplace transform, of μ on certain linear manifolds associated with B. The proof of our result makes an essential use of the necessary and sufficient condition derived in [12]. Several applications to specific situations are discussed. Particularly, it is shown that if the support of μ is small enough then linear independence is guaranteed provided that does not vanish at a certain finite set of critical points associated with B. Also, the results here provide a new proof of the linear independence condition for the translates of B itself.

scholarly journals Algebraic independence properties of the Fredholm series

1978 ◽  
Vol 26 (1) ◽  
pp. 31-45 ◽  
Author(s):  
J. H. Loxton ◽  
A. J. van der Poorten
Keyword(s):  
Algebraic Independence ◽  
Rational Functions ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Algebraic Numbers ◽  
Independence Properties ◽  
Image Position ◽  
Necessary And Sufficient

AbstractWe consider algebraic independence properties of series such as We show that the functions fr(z) are algebraically independent over the rational functions Further, if αrs (r = 2, 3, 4, hellip; s = 1, 2, 3, hellip) are algebraic numbers with 0 < |αrs|, we obtain an explicit necessary and sufficient condition for the algebraic independence of the numbers fr(αrs) over the rationals.

scholarly journals A LIMIT THEOREM FOR OCCUPATION MEASURES OF LÉVY PROCESSES IN COMPACT GROUPS

2012 ◽  
Vol 13 (01) ◽  
pp. 1250008
Author(s):  
ARNO BERGER ◽  
STEVEN N. EVANS
Keyword(s):  
Limit Theorem ◽  
Dynamical Systems ◽  
Compact Group ◽  
Short Proof ◽  
Compact Groups ◽  
Sufficient Condition ◽  
Occupation Measure ◽  
Necessary And Sufficient Condition ◽  
Occupation Measures ◽  
Necessary And Sufficient

A short proof utilizing dynamical systems techniques is given of a necessary and sufficient condition for the normalized occupation measure of a Lévy process in a metrizable compact group to be asymptotically uniform with probability one.

scholarly journals On linear independence of trigonometric numbers

2018 ◽  
Vol 34 (2) ◽  
pp. 157-166
Author(s):  
ARNO BERGER ◽  
Keyword(s):  
Linear Independence ◽  
Number Fields ◽  
Rational Numbers ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Necessary And Sufficient

A necessary and sufficient condition is established for 1, cos(πr1), and cos(πr2) to be rationally independent, where r1, r2 are rational numbers. The elementary computational argument yields linear independence over larger number fields as well.

A Proposed Framework Emphasizing Auditor Reliability over Auditor Independence

2003 ◽  
Vol 17 (3) ◽  
pp. 257-266 ◽  
Author(s):  
Mark H. Taylor ◽  
F. Todd DeZoort ◽  
Edward Munn ◽  
Martha Wetterhall Thomas
Keyword(s):  
Public Interest ◽  
Auditor Independence ◽  
Public Confidence ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Accounting Profession ◽  
The Public ◽  
Necessary And Sufficient

This paper introduces an auditor reliability framework that repositions the role of auditor independence in the accounting profession. The framework is motivated in part by widespread confusion about independence and the auditing profession's continuing problems with managing independence and inspiring public confidence. We use philosophical, theoretical, and professional arguments to argue that the public interest will be best served by reprioritizing professional and ethical objectives to establish reliability in fact and appearance as the cornerstone of the profession, rather than relationship-based independence in fact and appearance. This revised framework requires three foundation elements to control subjectivity in auditors' judgments and decisions: independence, integrity, and expertise. Each element is a necessary but not sufficient condition for maximizing objectivity. Objectivity, in turn, is a necessary and sufficient condition for achieving and maintaining reliability in fact and appearance.

The Power of Public Positions

2018 ◽  
Author(s):  
Thomas Sinclair
Keyword(s):  
Detailed Analysis ◽  
Political Authority ◽  
The State ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
State Institutions ◽  
State Of Nature ◽  
Necessary And Sufficient

The Kantian account of political authority holds that the state is a necessary and sufficient condition of our freedom. We cannot be free outside the state, Kantians argue, because any attempt to have the “acquired rights” necessary for our freedom implicates us in objectionable relations of dependence on private judgment. Only in the state can this problem be overcome. But it is not clear how mere institutions could make the necessary difference, and contemporary Kantians have not offered compelling explanations. A detailed analysis is presented of the problems Kantians identify with the state of nature and the objections they face in claiming that the state overcomes them. A response is sketched on behalf of Kantians. The key idea is that under state institutions, a person can make claims of acquired right without presupposing that she is by nature exceptional in her capacity to bind others.

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