Ergodic properties of some inverse polynomial series expansions of laurent series

1992 ◽  
Vol 60 (3-4) ◽  
pp. 241-246 ◽  
Author(s):  
J. Knopfmacher
Keyword(s):  
Laurent Series ◽  
Series Expansions ◽  
Ergodic Properties ◽  
Polynomial Series

scholarly journals Laurent series expansions of multiple zeta-functions of Euler–Zagier type at integer points

2019 ◽  
Vol 295 (1-2) ◽  
pp. 623-642
Author(s):  
Kohji Matsumoto ◽  
Tomokazu Onozuka ◽  
Isao Wakabayashi
Keyword(s):  
Laurent Series ◽  
Zeta Functions ◽  
Series Expansions ◽  
Integer Points ◽  
Multiple Zeta

Modeling potential flow using Laurent series expansions and boundary elements

2010 ◽  
Vol 28 (2) ◽  
pp. 573-586 ◽  
Author(s):  
T.R. Dean ◽  
T.V. Hromadka ◽  
Thomas Kastner ◽  
Michael Phillips
Keyword(s):  
Potential Flow ◽  
Laurent Series ◽  
Boundary Elements ◽  
Series Expansions

scholarly journals Corrigendum: ‘On certain algebraic curves related to polynomial maps, Compositio Math. 103 (1996), 319–350’

2010 ◽  
Vol 147 (1) ◽  
pp. 332-334 ◽  
Author(s):  
Patrick Morton
Keyword(s):  
Finite Field ◽  
Laurent Series ◽  
Algebraic Curves ◽  
Periodic Points ◽  
Series Expansions ◽  
Rational Field ◽  
Polynomial Maps ◽  
Polynomial Map ◽  
Hensel’S Lemma ◽  
Compositio Math

AbstractAn argument is given to fill a gap in a proof in the author’s article On certain algebraic curves related to polynomial maps, Compositio Math. 103 (1996), 319–350, that the polynomial Φn(x,c), whose roots are the periodic points of period n of a certain polynomial map x→f(x,c), is absolutely irreducible over the finite field of p elements, provided that f(x,1) has distinct roots and that the multipliers of the orbits of period n are also distinct over $\mathbb { F}_p$. Assuming that Φn(x,c) is reducible in characteristic p, we show that Hensel’s lemma and Laurent series expansions of the roots can be used to obtain a factorization of Φn(x,c) in characteristic 0, contradicting the absolute irreducibility of this polynomial over the rational field.

scholarly journals Engel Series Expansions of Laurent Series and Hausdorff Dimensions

2003 ◽  
Vol 75 (1) ◽  
pp. 1-7 ◽  
Author(s):  
Jun Wu
Keyword(s):  
Hausdorff Dimension ◽  
Positive Integer ◽  
Power Series ◽  
Finite Field ◽  
Formal Power Series ◽  
Laurent Series ◽  
Series Expansions ◽  
Formal Laurent Series ◽  
Hausdorff Dimensions ◽  
Formal Power

AbstractFor any positive integer q≧2, let Fq be a finite field with q elements, Fq ((z-1)) be the field of all formal Laurent series in an inderminate z, I denote the valuation ideal z-1Fq [[z-1]] in the ring of formal power series Fq ((z-1)) normalized by P(l) = 1. For any x ∈ I, let the series be the Engel expansin of Laurent series of x. Grabner and Knopfmacher have shown that the P-measure of the set A(α) = {x ∞ I: limn→∞ deg an(x)/n = ά} is l when α = q/(q -l), where deg an(x) is the degree of polynomial an(x). In this paper, we prove that for any α ≧ l, A(α) has Hausdorff dimension l. Among other thing we also show that for any integer m, the following set B(m) = {x ∈ l: deg an+1(x) - deg an(x) = m for any n ≧ l} has Hausdorff dimension 1.

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