Index-Dependent Parameters of Laguerre and Related Polynomial Sets

1970 ◽  
Vol 25 (4) ◽  
pp. 852
Author(s):  
J. W. Brown ◽  
J. L. Goldberg
Keyword(s):  
Related Polynomial

scholarly journals NONSOLVABLE POLYNOMIALS WITH FIELD DISCRIMINANT 5A

2011 ◽  
Vol 07 (02) ◽  
pp. 289-322
Author(s):  
DAVID P. ROBERTS
Keyword(s):  
Galois Group ◽  
Class Number ◽  
Related Polynomial

We present the first explicitly known polynomials in Z[x] with nonsolvable Galois group and field discriminant of the form ±pA for p ≤ 7 a prime. Our main polynomial has degree 25, Galois group of the form PSL2(5)5.10, and field discriminant 569. A closely related polynomial has degree 120, Galois group of the form SL2(5)5.20, and field discriminant 5311. We completely describe 5-adic behavior, finding in particular that the root discriminant of both splitting fields is 125 · 5-1/12500 ≈ 124.984 and the class number of the latter field is divisible by 54.

scholarly journals Super-representations of quivers and related polynomial semi-invariants

2020 ◽  
Vol 30 (04) ◽  
pp. 883-902
Author(s):  
V. A. Bovdi ◽  
A. N. Zubkov
Keyword(s):  
Characteristic Zero ◽  
Polynomial Invariants ◽  
Representations Of Quivers ◽  
Related Polynomial

We introduce the notion of a super-representation of a quiver. For super-representations of quivers over a field of characteristic zero, we describe the corresponding (super)algebras of polynomial semi-invariants and polynomial invariants.

scholarly journals Martingale estimation functions for Bessel processes

2021 ◽  
Author(s):  
Nicole Hufnagel ◽  
Jeannette H. C. Woerner
Keyword(s):  
Bessel Process ◽  
Estimating Function ◽  
Estimating Functions ◽  
Bessel Processes ◽  
One Dimensional ◽  
Diffusion Operator ◽  
Related Polynomial ◽  
Martingale Estimating Function ◽  
Ergodic Diffusions ◽  
First Eigenfunction

AbstractIn this paper we derive martingale estimating functions for the dimensionality parameter of a Bessel process based on the eigenfunctions of the diffusion operator. Since a Bessel process is non-ergodic and the theory of martingale estimating functions is developed for ergodic diffusions, we use the space-time transformation of the Bessel process and formulate our results for a modified Bessel process. We deduce consistency, asymptotic normality and discuss optimality. It turns out that the martingale estimating function based of the first eigenfunction of the modified Bessel process coincides with the linear martingale estimating function for the Cox Ingersoll Ross process. Furthermore, our results may also be applied to estimating the multiplicity parameter of a one-dimensional Dunkl process and some related polynomial processes.

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