Distribution of Dirichlet L-functions with real characters in the half-plane Re s&gt;1/2

Stankus, Eugenijus

doi:10.1007/bf00969798

Cited by 6 publications

(3 citation statements)

References 8 publications

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“…for σ > 3/4, where a is any positive real number. Similar results for L-functions of degree one were proved by Barban [1], Elliott [8][9][10][11], Stankus [35,36], and others.…”

Section: Introduction and Statement Of Resultssupporting

confidence: 81%

Probability density functions attached to random Euler products for automorphic $L$-functions

Mine

2020

Preprint

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In this paper, we study the value-distributions of L-functions of holomorphic primitive cusp forms in the level aspect. We associate such automorphic L-functions with probabilistic models called the random Euler products. First, we prove the existence of probability density functions attached to the random Euler products. Then various mean values of automorphic L-functions are expressed as integrals involving the density functions. Moreover, we estimate the discrepancies between the distributions of values of automorphic L-functions and those of the random Euler products.

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“…for σ > 3/4, where a is any positive real number. Similar results for L-functions of degree one were proved by Barban [1], Elliott [8][9][10][11], Stankus [35,36], and others.…”

Section: Introduction and Statement Of Resultssupporting

confidence: 81%

Probability density functions attached to random Euler products for automorphic $L$-functions

Mine

2020

Preprint

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“…It follows that L^(Ä)>0 for almost all D. The same problem for Re s> 1/2 was studied by Elliott in several papers (see e.g. [2]); some of his results were generalized by Stankus [9]. Elliott considered the distribution of the modulus and argument of (for prime moduli), and Stankus proved that Lß{s) belongs to a given Borel set A in the complex plane with a certain probability depending on 5 and A.…”

Section: Introduction and Statement Of Resultsmentioning

confidence: 87%

On the Mean Value of L(1/2, χ ) FW Real Characters

Jutila¹

1981

Analysis

132

129

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“…It is a profound problem in analytic number theory to understand the distribution of values of L(s, χ p ), the Dirichlet L-functions associated to the quadratic character χ p , for fixed s and variable p, where for a prime number p ≡ v (mod 4) with v = 1 or 3, the quadratic character χ p (n) is defined by the Legendre symbol χ p (n) = ( n p ). The problem about the distribution of values of Dirichlet L-functions with real characters χ modulo a prime p was first studied by Elliott in [9] and later some of his results were generalized by Stankus [18].…”

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confidence: 99%

Average values of L-series for real characters in function fields

2016

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We establish asymptotic formulae for the first and second moments of quadratic Dirichlet L-functions, at the center of the critical strip, associated to the real quadratic function field k( √ P) and inert imaginary quadratic function field k( γ P) with P being a monic irreducible polynomial over a fixed finite field F q of odd cardinality q and γ a generator of F × q . We also study mean values for the class number and for the cardinality of the second K -group of maximal order of the associated fields for ramified imaginary, real, and inert imaginary quadratic function fields over F q . One of the main novelties of this paper is that we compute the second moment of quadratic Dirichlet L-functions associated to monic irreducible polynomials. It is worth noting that the similar second moment over number fields is unknown. The second innovation of this paper comes from the fact that, if the cardinality of the ground field is even then the task of average L-functions in function fields is much harder and, in this paper, we are able to handle this strenuous case and establish several mean values results of L-functions over function fields.

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Distribution of Dirichlet L-functions with real characters in the half-plane Re s>1/2

Cited by 6 publications

References 8 publications

Probability density functions attached to random Euler products for automorphic $L$-functions

Probability density functions attached to random Euler products for automorphic $L$-functions

On the Mean Value of L(1/2, χ ) FW Real Characters

Average values of L-series for real characters in function fields

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