scholarly journals Greatest prime divisors of polynomial values over function fields

2014 ◽  
Vol 165 (4) ◽  
pp. 339-349
Author(s):  
Alexei Entin
Keyword(s):  
Function Fields ◽  
Prime Divisors

STATISTICS OF PRIME DIVISORS IN FUNCTION FIELDS

2009 ◽  
Vol 05 (01) ◽  
pp. 141-152 ◽  
Author(s):  
ROBERT C. RHOADES
Keyword(s):  
Simple Proof ◽  
Function Field ◽  
Function Fields ◽  
Random Polynomial ◽  
Prime Divisors ◽  
Number Of Prime Divisors ◽  
Field Setting ◽  
The Way

We show that the prime divisors of a random polynomial in 𝔽q[t] are typically "Poisson distributed". This result is analogous to the result in ℤ of Granville [1]. Along the way, we use a sieve developed by Granville and Soundararajan [2] to give a simple proof of the Erdös–Kac theorem in the function field setting. This approach gives stronger results about the moments of the sequence {ω(f)}f∈𝔽q[t] than was previously known, where ω(f) is the number of prime divisors of f.

scholarly journals ON THE GROWTH OF LINEAR RECURRENCES IN FUNCTION FIELDS

2020 ◽  
pp. 1-10
Author(s):  
CLEMENS FUCHS ◽  
SEBASTIAN HEINTZE
Keyword(s):  
Number Field ◽  
Function Field ◽  
Function Fields ◽  
Linear Recurrence ◽  
Recurrence Sequence ◽  
Linear Recurrences ◽  
Field Case ◽  
Power Sum ◽  
Linear Recurrence Sequence

Abstract Let $ (G_n)_{n=0}^{\infty } $ be a nondegenerate linear recurrence sequence whose power sum representation is given by $ G_n = a_1(n) \alpha _1^n + \cdots + a_t(n) \alpha _t^n $ . We prove a function field analogue of the well-known result in the number field case that, under some nonrestrictive conditions, $ |{G_n}| \geq ( \max _{j=1,\ldots ,t} |{\alpha _j}| )^{n(1-\varepsilon )} $ for $ n $ large enough.

scholarly journals A new characterization of L2(p2)

2020 ◽  
Vol 18 (1) ◽  
pp. 907-915
Author(s):  
Zhongbi Wang ◽  
Chao Qin ◽  
Heng Lv ◽  
Yanxiong Yan ◽  
Guiyun Chen
Keyword(s):  
Positive Integer ◽  
Irreducible Character ◽  
Character Degrees ◽  
Prime Divisors

Abstract For a positive integer n and a prime p, let {n}_{p} denote the p-part of n. Let G be a group, \text{cd}(G) the set of all irreducible character degrees of G , \rho (G) the set of all prime divisors of integers in \text{cd}(G) , V(G)=\left\{{p}^{{e}_{p}(G)}|p\in \rho (G)\right\} , where {p}^{{e}_{p}(G)}=\hspace{.25em}\max \hspace{.25em}\{\chi {(1)}_{p}|\chi \in \text{Irr}(G)\}. In this article, it is proved that G\cong {L}_{2}({p}^{2}) if and only if |G|=|{L}_{2}({p}^{2})| and V(G)=V({L}_{2}({p}^{2})) .

On geometric Z p -extensions of function fields

1988 ◽  
Vol 62 (2) ◽  
pp. 145-161 ◽  
Author(s):  
R. Gold ◽  
H. Kisilevsky
Keyword(s):  
Function Fields
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