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Diaconu, Adrian

doi:10.1016/j.jnt.2018.09.023

Cited by 23 publications

(28 citation statements)

References 30 publications

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“…Proof. The proof is similar to that of [22,Lemma 6.5]. We first show that the series ( 41) is absolutely convergent when R(s i ) is sufficiently large.…”

Section: Wmds Associated To Moments Of L-seriesmentioning

confidence: 63%

“…Proof. We found an explicit non-singular matrix A 0 (x; u) of the form (22) with polynomial entries in x, u satisfying (23), and the interested reader can find it in [1]. Thus we have the corresponding extensions of the cocycle Λ, and of the Chinta-Gunnells action, to all of W ⊕ Z.…”

Section: An Extension Of the Chinta-gunnells Actionmentioning

confidence: 99%

“…A conjectural asymptotic formula, for all r, was first given by Andrade and Keating [2] (see also [43]), and a refined version, exhibiting additional lower order terms in the asymptotic formula, was recently proposed in [26]. This conjecture is known only for r ⩽ 3, see [28,29,22], and when r = 4, a weaker form of the asymptotic formula is known by the work of Florea [30].…”

Section: Introductionmentioning

confidence: 99%

“…-There exists an invertible matrix A(x; u) of the form(22) satisfying the following conditions: The cocycle relation(23) is satisfied.…”

mentioning

confidence: 99%

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Quadratic Weyl group multiple Dirichlet series of Type $D_{\scriptscriptstyle 4}^{\scriptscriptstyle (1)}$

Diaconu¹,

Paşol²,

Popa³

2021

Preprint

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In this paper and its sequel [25], we investigate the precise relationship between the quadratic affine Weyl group multiple Dirichlet series in the sense of [18,12], and those defined axiomatically by Whitehead [46] and [45]. In particular, we show that the axiomatic quadratic Weyl group multiple Dirichlet series of type D (1) 4 over rational function fields of odd characteristic admits meromorphic continuation to the interior of the corresponding complexified Tits cone. We shall also determine the polar divisor of this function, and compute the residue at each of its poles. As a consequence, we obtain an exact formula for a weighted 4-th moment of quadratic Dirichlet L-functions over rational function fields; we shall also derive an asymptotic formula for this weighted moment that is expected to generalize to any global field.

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“…Proof. The proof is similar to that of [22,Lemma 6.5]. We first show that the series ( 41) is absolutely convergent when R(s i ) is sufficiently large.…”

Section: Wmds Associated To Moments Of L-seriesmentioning

confidence: 63%

Section: An Extension Of the Chinta-gunnells Actionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…-There exists an invertible matrix A(x; u) of the form(22) satisfying the following conditions: The cocycle relation(23) is satisfied.…”

mentioning

confidence: 99%

See 2 more Smart Citations

Quadratic Weyl group multiple Dirichlet series of Type $D_{\scriptscriptstyle 4}^{\scriptscriptstyle (1)}$

Diaconu¹,

Paşol²,

Popa³

2021

Preprint

Self Cite

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show abstract

“…It is important to observe that Diaconu et al [16] have also conjectured moments of families of L-functions using different techniques. Their method is based on multiple Dirichlet series.…”

Section: Introductionmentioning

confidence: 99%

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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Ratios conjecture for quadratic Hecke L-functions in the Gaussian field

Gao,

Zhao

2023

Monatsh Math

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We develop the L-functions ratios conjecture with one shift in the numerator and denominator in certain ranges for the family of quadratic Hecke L-functions in the Gaussian field using multiple Dirichlet series under the generalized Riemann hypothesis. We also obtain an asymptotical formula for the first moment of central values of the same family of L-functions, obtaining an error term of size $$O(X^{1/2+\varepsilon })$$ O ( X 1 / 2 + ε ) .

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On the third moment of L(12,χd)

Cited by 23 publications

References 30 publications

Quadratic Weyl group multiple Dirichlet series of Type $D_{\scriptscriptstyle 4}^{\scriptscriptstyle (1)}$

Quadratic Weyl group multiple Dirichlet series of Type $D_{\scriptscriptstyle 4}^{\scriptscriptstyle (1)}$

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

Ratios conjecture for quadratic Hecke L-functions in the Gaussian field

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