Moments of Dirichlet L–functions with prime conductors over function fields

Bui, H. M.; Florea, Alexandra

doi:10.1016/j.ffa.2020.101659

Cited by 4 publications

(3 citation statements)

References 22 publications

(27 reference statements)

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“…In a recent paper, Andrade, Jung and Shamesaldeen [2] conjectured the integral moments and ratios of quadratic Dirichlet L-functions over monic irreducible polynomials in F q [T ] and showed that their conjecture agrees with the asymptotic formulas obtained by Andrade and Keating [4] and Bui and Florea [8].…”

Section: If We Letmentioning

confidence: 87%

Conjectures for the Integral Moments and Ratios of L-functions in Even characteristic

MacMillan

2021

Preprint

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In this paper, we extend to the function field setting the heuristics developed by Conrey, Farmer, Keating, Rubinstein and Snaith for the integral moments of L-functions. Also, we adapt to function field setting the heuristics first developed by Conrey, Farmer and Zirnbauer to the study of mean values of ratios of L-functions. Specifically, we obtain an asymptotic formula for the integral moments and ratios of the quadratic Dirichlet L-functions L(s, χ u ) over the rational function field F q (T ), when q is a power of 2 and over a given family. As an application, we calculate the one-level density for the zeros of these L-functions.

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Section: If We Letmentioning

confidence: 87%

Conjectures for the Integral Moments and Ratios of L-functions in Even characteristic

MacMillan

2021

Preprint

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“…Recently, Bui and Florea [6] improved Andrade and Keating's result for the second moment and proved that…”

Section: The Function Field Settingmentioning

confidence: 89%

The integral moments and ratios of quadratic Dirichlet L-functions over monic irreducible polynomials in $$\mathbb {F}_{q}[T]$$

2021

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In this paper, we extend to the function field setting the heuristics formerly developed by Conrey, Farmer, Keating, Rubinstein and Snaith, for the integral moments of L-functions. We also adapt to the function field setting the heuristics first developed by Conrey, Farmer and Zirnbauer to the study of mean values of ratios of L-functions. Specifically, the focus of this paper is on the family of quadratic Dirichlet L-functions $$L(s,\chi _{P})$$ L ( s , χ P ) where the character $$\chi $$ χ is defined by the Legendre symbol for polynomials in $$\mathbb {F}_{q}[T]$$ F q [ T ] with $$\mathbb {F}_{q}$$ F q a finite field of odd cardinality, and the averages are taken over all monic and irreducible polynomials P of a given odd degree. As an application, we also compute the formula for the one-level density for the zeros of these L-functions.

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“…, χ P ∼ P log q P , while, along with Bui and Florea [5], in the same paper computed the second moment…”

Section: Introductionmentioning

confidence: 93%

Rudnick and Soundarajan's Theorem over Prime Polynomials for the Rational Function Field

MacMillan¹

2020

Preprint

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Moments of Dirichlet L–functions with prime conductors over function fields

Cited by 4 publications

References 22 publications

Conjectures for the Integral Moments and Ratios of L-functions in Even characteristic

Conjectures for the Integral Moments and Ratios of L-functions in Even characteristic

The integral moments and ratios of quadratic Dirichlet L-functions over monic irreducible polynomials in $$\mathbb {F}_{q}[T]$$

Rudnick and Soundarajan's Theorem over Prime Polynomials for the Rational Function Field

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