Eigenvalues in the large sieve inequality, II

Ramaré, Olivier

doi:10.5802/jtnb.710

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Influence Of the Riemann Hypothesis1

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2023

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“…N . The values for the even moments of this limit distribution reveals that it is not a classical distribution, confirming what the (rather limited) computations from [36].…”

Section: Influence Of the Riemann Hypothesissupporting

confidence: 81%

A spectral resolution of the large sieve

Ramaré¹

2023

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The quadratic form V pϕ, Qq " ř q"Q ř a mod ˚q |Spϕ, a{qq| 2 and its eigenvalues are well understood when Q " op ? N q, while V pϕ, Qq is expected to behave like a Riemann sum when N " opQq. The behavior in the range Q P r ? N , 100N s is still mysterious. In the present work we present a full spectral analysis when Q ě N 7{8 in terms of the eigenvalues of a one-parameter family of nuclear difference operators. We show in particular that (a smoothed version of) the quadratic form V pϕ, Qq may stay away from p6{π 2 qQ ř n |ϕn| 2 when Q -N , though only on a vector space of positive but small dimension.

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“…N . The values for the even moments of this limit distribution reveals that it is not a classical distribution, confirming what the (rather limited) computations from [36].…”

Section: Influence Of the Riemann Hypothesissupporting

confidence: 81%

A spectral resolution of the large sieve

Ramaré¹

2023

Preprint

View full text Add to dashboard Cite

show abstract

Eigenvalues in the large sieve inequality, II

Cited by 1 publication

References 26 publications

A spectral resolution of the large sieve

A spectral resolution of the large sieve

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