Continued $$\beta $$ β -fractions with formal power series over finite fields

2015 ◽  
Vol 39 (1) ◽  
pp. 95-105
Author(s):  
M. Hbaib ◽  
R. Kammoun
Keyword(s):  
Power Series ◽  
Formal Power Series ◽  
Finite Fields ◽  
Formal Power

ON TRANSCENDENTAL CONTINUED FRACTIONS IN FIELDS OF FORMAL POWER SERIES OVER FINITE FIELDS

2021 ◽  
pp. 1-12
Author(s):  
BÜŞRA CAN ◽  
GÜLCAN KEKEÇ
Keyword(s):  
Power Series ◽  
Finite Field ◽  
Formal Power Series ◽  
Finite Fields ◽  
Continued Fractions ◽  
Continued Fraction ◽  
Continued Fraction Expansions ◽  
Formal Power

Abstract In the field of formal power series over a finite field, we prove a result which enables us to construct explicit examples of $U_{m}$ -numbers by using continued fraction expansions of algebraic formal power series of degree $m>1$ .

-NUMBERS IN FIELDS OF FORMAL POWER SERIES OVER FINITE FIELDS

2019 ◽  
Vol 101 (2) ◽  
pp. 218-225
Author(s):  
GÜLCAN KEKEÇ
Keyword(s):  
Power Series ◽  
Finite Field ◽  
Formal Power Series ◽  
Finite Fields ◽  
Finite Extension ◽  
Formal Power

In the field $\mathbb{K}$ of formal power series over a finite field $K$, we consider some lacunary power series with algebraic coefficients in a finite extension of $K(x)$. We show that the values of these series at nonzero algebraic arguments in $\mathbb{K}$ are $U$-numbers.

Formal power series and nearly analytic functions

1991 ◽  
Vol 57 (1) ◽  
pp. 61-70 ◽  
Author(s):  
H�kan Hedenmalm
Keyword(s):  
Power Series ◽  
Formal Power Series ◽  
Analytic Functions ◽  
Formal Power

scholarly journals On transformations of formal power series

2003 ◽  
Vol 184 (2) ◽  
pp. 369-383 ◽  
Author(s):  
Manfred Droste ◽  
Guo-Qiang Zhang
Keyword(s):  
Power Series ◽  
Formal Power Series ◽  
Formal Power

scholarly journals On the Square Root of a Bell Matrix

2021 ◽  
Vol 76 (1) ◽  
Author(s):  
Donatella Merlini
Keyword(s):  
Power Series ◽  
Closed Form ◽  
Formal Power Series ◽  
Computational Method ◽  
Square Root ◽  
Riordan Arrays ◽  
Formal Power

AbstractIn the context of Riordan arrays, the problem of determining the square root of a Bell matrix $$R={\mathcal {R}}(f(t)/t,\ f(t))$$ R = R ( f ( t ) / t , f ( t ) ) defined by a formal power series $$f(t)=\sum _{k \ge 0}f_kt^k$$ f ( t ) = ∑ k ≥ 0 f k t k with $$f(0)=f_0=0$$ f ( 0 ) = f 0 = 0 is presented. It is proved that if $$f^\prime (0)=1$$ f ′ ( 0 ) = 1 and $$f^{\prime \prime }(0)\ne 0$$ f ″ ( 0 ) ≠ 0 then there exists another Bell matrix $$H={\mathcal {R}}(h(t)/t,\ h(t))$$ H = R ( h ( t ) / t , h ( t ) ) such that $$H*H=R;$$ H ∗ H = R ; in particular, function h(t) is univocally determined by a symbolic computational method which in many situations allows to find the function in closed form. Moreover, it is shown that function h(t) is related to the solution of Schröder’s equation. We also compute a Riordan involution related to this kind of matrices.

On the intersection of null spaces for matrix substitutions in a non-commutative rational formal power series

2004 ◽  
Vol 339 (8) ◽  
pp. 533-538 ◽  
Author(s):  
Daniel Alpay ◽  
Dmitry S. Kalyuzhnyı̆-Verbovetzkiı̆
Keyword(s):  
Power Series ◽  
Formal Power Series ◽  
Formal Power

scholarly journals Two Interacting Coordinate Hopf Algebras of Affine Groups of Formal Series on a Category

Algebra ◽  
2013 ◽  
Vol 2013 ◽  
pp. 1-10
Author(s):  
Laurent Poinsot
Keyword(s):  
Power Series ◽  
Formal Power Series ◽  
Semidirect Product ◽  
Hopf Algebras ◽  
Formal Series ◽  
Product Structure ◽  
Locally Finite ◽  
Commutative Algebras ◽  
Affine Groups ◽  
Formal Power

A locally finite category is defined as a category in which every arrow admits only finitely many different ways to be factorized by composable arrows. The large algebra of such categories over some fields may be defined, and with it a group of invertible series (under multiplication). For certain particular locally finite categories, a substitution operation, generalizing the usual substitution of formal power series, may be defined, and with it a group of reversible series (invertible under substitution). Moreover, both groups are actually affine groups. In this contribution, we introduce their coordinate Hopf algebras which are both free as commutative algebras. The semidirect product structure obtained from the action of reversible series on invertible series by anti-automorphisms gives rise to an interaction at the level of their coordinate Hopf algebras under the form of a smash coproduct.

Cyclic codes over formal power series rings

2011 ◽  
Vol 31 (1) ◽  
pp. 331-343 ◽  
Author(s):  
Steven T. Dougherty ◽  
Liu Hongwei
Keyword(s):  
Power Series ◽  
Formal Power Series ◽  
Cyclic Codes ◽  
Power Series Rings ◽  
Formal Power
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