On the density of irreducible polynomials which generate k-free polynomials over function fields

Extremal behaviour of ± 1-valued completely multiplicative functions in function fields

Glasnik Matematicki ◽

10.3336/gm.56.1.06 ◽

2021 ◽

Vol 56 (1) ◽

pp. 79-94

Author(s):

Nikola Lelas ◽

Keyword(s):

Rational Function ◽

Finite Fields ◽

Function Fields ◽

Mean Value ◽

Multiplicative Functions ◽

Irreducible Polynomials ◽

Liouville Function ◽

The Mean

We investigate the classical Pólya and Turán conjectures in the context of rational function fields over finite fields 𝔽q. Related to these two conjectures we investigate the sign of truncations of Dirichlet L-functions at point s=1 corresponding to quadratic characters over 𝔽q[t], prove a variant of a theorem of Landau for arbitrary sets of monic, irreducible polynomials over 𝔽q[t] and calculate the mean value of certain variants of the Liouville function over 𝔽q[t].

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THE RECIPROCITY LAW FOR THE TWISTED SECOND MOMENT OF DIRICHLET -FUNCTIONS OVER RATIONAL FUNCTION FIELDS

Bulletin of the Australian Mathematical Society ◽

10.1017/s0004972718000874 ◽

2018 ◽

Vol 98 (3) ◽

pp. 383-388 ◽

Cited By ~ 2

Author(s):

GORAN DJANKOVIĆ

Keyword(s):

Rational Function ◽

Function Fields ◽

Mean Square ◽

Irreducible Polynomials ◽

Second Moment ◽

Reciprocity Law ◽

Second Moments ◽

The Mean

We prove the reciprocity law for the twisted second moments of Dirichlet $L$-functions over rational function fields, corresponding to two irreducible polynomials. This formula is the analogue of the formulas for Dirichlet $L$-functions over $\mathbb{Q}$ obtained by Conrey [‘The mean-square of Dirichlet $L$-functions’, arXiv:0708.2699 [math.NT] (2007)] and Young [‘The reciprocity law for the twisted second moment of Dirichlet $L$-functions’, Forum Math. 23(6) (2011), 1323–1337].

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The moments and statistical distribution of class number of primes over function fields

Finite Fields and Their Applications ◽

10.1016/j.ffa.2021.101845 ◽

2021 ◽

Vol 73 ◽

pp. 101845

Author(s):

Julio Andrade ◽

Asmaa Shamesaldeen

Keyword(s):

Class Number ◽

Function Fields ◽

Statistical Distribution

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1. Finite Fields and Function Fields

Algebraic Geometry in Coding Theory and Cryptography ◽

10.1515/9781400831302-002 ◽

2010 ◽

pp. 1-29

Keyword(s):

Finite Fields ◽

Function Fields ◽

And Function

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ON THE GROWTH OF LINEAR RECURRENCES IN FUNCTION FIELDS

Bulletin of the Australian Mathematical Society ◽

10.1017/s0004972720001094 ◽

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.

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