Zero-density estimate of L-functions attached to Maass forms

Sankaranarayanan, A.; Sengupta, Jyoti

doi:10.4064/aa127-3-5

Cited by 16 publications

(4 citation statements)

References 15 publications

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“…This assumption has been proved for a wide range of L-functions. Indeed it holds for all elements of the Selberg Class S by the work of Kaczorowski and Perelli [11], and for L-functions attached to GL(2)-Maass cusp forms by the work of Sankaranarayanan and Sengupta [25]. We prove Theorem 3.…”

Section: Introduction and Statement Of Resultsmentioning

confidence: 82%

Distribution of values of L -functions at the edge of the critical strip

Lamzouri

2009

Proceedings of the London Mathematical Society

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We prove several results on the distribution of values of L‐functions at the edge of the critical strip, by constructing and studying a large class of random Euler products. Among new applications, we study families of symmetric power L‐functions of holomorphic cusp forms in the level aspect (assuming the automorphy of these L‐functions) at s = 1, functions in the Selberg class (in the height aspect) and quadratic twists of a fixed GL(m)/ℚ‐automorphic cusp form at s = 1.

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Section: Introduction and Statement Of Resultsmentioning

confidence: 82%

Distribution of values of L -functions at the edge of the critical strip

Lamzouri

2009

Proceedings of the London Mathematical Society

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“…The key ingredients to prove the above lemma are followed from [13, p. 102, Fomula 5.24] and [18,Lemma 3.6]. One can therefore apply the similar argument as in [20, p. 219, Section 9.8] or [9, p. 6] to complete the proof.…”

Section: Transformation Formula Involving the Non-trivial Zeros Of L(...mentioning

confidence: 93%

Equivalent criterion for the grand Riemann hypothesis associated to Maass cusp forms

Banerjee¹,

Kumar²

2021

Preprint

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“…Here we take the Riemann zeta function ζ(s) as an example of the automorphic Lfunction L(s, π). To specify π by cusp forms and Maass forms, we refer to the references [16][17][18] and references therein. From the works of Ingham [19] and Huxley [20] we know that…”

Section: Introductionmentioning

confidence: 99%

New Zero-Density Results for Automorphic L-Functions of GL(n)

2021

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Let L(s,π) be an automorphic L-function of GL(n), where π is an automorphic representation of group GL(n) over rational number field Q. In this paper, we study the zero-density estimates for L(s,π). Define Nπ(σ,T1,T2) = ♯ {ρ = β + iγ: L(ρ,π) = 0, σ<β<1, T1≤γ≤T2}, where 0≤σ<1 and T1<T2. We first establish an upper bound for Nπ(σ,T,2T) when σ is close to 1. Then we restrict the imaginary part γ into a narrow strip [T,T+Tα] with 0<α≤1 and prove some new zero-density results on Nπ(σ,T,T+Tα) under specific conditions, which improves previous results when σ near 34 and 1, respectively. The proofs rely on the zero detecting method and the Halász-Montgomery method.

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Zero-density estimate of L-functions attached to Maass forms

Cited by 16 publications

References 15 publications

Distribution of values of L -functions at the edge of the critical strip

Distribution of values of L -functions at the edge of the critical strip

Equivalent criterion for the grand Riemann hypothesis associated to Maass cusp forms

New Zero-Density Results for Automorphic L-Functions of GL(n)

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