scholarly journals Generalization of Pólya’s Zero Distribution Theory for Exponential Polynomials, and Sharp Results for Asymptotic Growth

2020 ◽  
Author(s):  
Janne M. Heittokangas ◽  
Zhi-Tao Wen
Keyword(s):  
Distribution Theory ◽  
Exponential Polynomials ◽  
Asymptotic Growth ◽  
Zero Distribution

Zero distribution and division results for exponential polynomials

2018 ◽  
Vol 227 (1) ◽  
pp. 397-421 ◽  
Author(s):  
Janne Heittokangas ◽  
Katsuya Ishizaki ◽  
Kazuya Tohge ◽  
Zhi-Tao Wen
Keyword(s):  
Exponential Polynomials ◽  
Zero Distribution

Resolution of T. Ward's Question and the Israel–Finch Conjecture: Precise Analysis of an Integer Sequence Arising in Dynamics

2014 ◽  
Vol 24 (1) ◽  
pp. 195-215
Author(s):  
JEFFREY GAITHER ◽  
GUY LOUCHARD ◽  
STEPHAN WAGNER ◽  
MARK DANIEL WARD
Keyword(s):  
Weighted Average ◽  
Analytic Number Theory ◽  
Combinatorial Structure ◽  
Asymptotic Growth ◽  
First Order ◽  
Integer Sequence ◽  
Precise Analysis ◽  
Formula Group ◽  
Fourth Author ◽  
Image Position

We analyse the first-order asymptotic growth of \[ a_{n}=\int_{0}^{1}\prod_{j=1}^{n}4\sin^{2}(\pi jx)\, dx. \] The integer an appears as the main term in a weighted average of the number of orbits in a particular quasihyperbolic automorphism of a 2n-torus, which has applications to ergodic and analytic number theory. The combinatorial structure of an is also of interest, as the ‘signed’ number of ways in which 0 can be represented as the sum of ϵjj for −n ≤ j ≤ n (with j ≠ 0), with ϵj ∈ {0, 1}. Our result answers a question of Thomas Ward (no relation to the fourth author) and confirms a conjecture of Robert Israel and Steven Finch.

Distribution Theory and Transform Analysis

1968 ◽  
Vol 52 (379) ◽  
pp. 90
Author(s):  
D. S. Jones ◽  
A. H. Zemanian
Keyword(s):  
Distribution Theory

Kaldor’s Distribution Theory

1987 ◽  
Vol 9 (4) ◽  
pp. 572-575
Author(s):  
Joan O’Connell
Keyword(s):  
Distribution Theory
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