The least common multiple of random sets in polynomial rings over finite fields

被引：0

作者：

Djankovic, Goran ^{[1
]}

机构：

[1] Univ Belgrade, Fac Math, Studentski Trg 16,Pp 550, Belgrade 11000, Serbia

来源：

RAMANUJAN JOURNAL | 2021年 / 55卷 / 01期

关键词：

Least common multiple; Random sets; Finite fields; Function fields;

D O I：

10.1007/s11139-020-00357-9

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we investigate the distribution of degrees of the least common multiples of random subsets of monic polynomials of degree n in F-q[t]. We consider two different probabilistic models and find the concentration of degrees around the corresponding expectations when q -> infinity or n -> infinity.

引用

页码：13 / 23

页数：11

共 5 条

[1] IRREDUCIBLE POLYNOMIAL SETS AND DENSITY THEOREMS [J].

CAR, M .

ACTA ARITHMETICA, 1984, 44 (04) :323-342

[2] The least common multiple of random sets of positive integers [J].

Cilleruelo, Javier ;

Rue, Juanjo ;

Sarka, Paulius ;

Zumalacarregui, Ana .

JOURNAL OF NUMBER THEORY, 2014, 144 :92-104

[3] GAUSSIAN LIMITING DISTRIBUTIONS FOR THE NUMBER OF COMPONENTS IN COMBINATORIAL STRUCTURES [J].

FLAJOLET, P ;

SORIA, M .

JOURNAL OF COMBINATORIAL THEORY SERIES A, 1990, 53 (02) :165-182

[4] Mod-Poisson Convergence in Probability and Number Theory [J].

Kowalski, Emmanuel ;

Nikeghbali, Ashkan .

INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2010, 2010 (18) :3549-3587

[5] STATISTICS OF PRIME DIVISORS IN FUNCTION FIELDS [J].

Rhoades, Robert C. .

INTERNATIONAL JOURNAL OF NUMBER THEORY, 2009, 5 (01) :141-152

← 1 →