Tauberian Oscillation Theorems and the Distribution of Goldbach numbers

Bhowmik, Gautami; Ramaré, Olivier; Schlage‐Puchta, Jan‐Christoph

doi:10.5802/jtnb.940

Cited by 3 publications

(6 citation statements)

References 5 publications

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“…This is fairly close to optimal, since Bhowmik and Schlage-Puchta also proved that the error term here is Ω(x log log x). Analogous results for forms of (1.1), where n is written as the sum of k prime powers, have been proved by Languasco and Zaccagnini [12] and by Bhowmik, Ramaré, and Schlage-Puchta [1].…”

supporting

confidence: 59%

The size of oscillations in the Goldbach conjecture

Mossinghoff,

Trudgian

2020

Preprint

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Let R(n) = a+b=n Λ(a)Λ(b), where Λ(•) is the von Mangoldt function. The function R(n) is often studied in connection with Goldbach's conjecture. On the Riemann hypothesisand the sum is over the ordinates of the nontrivial zeros of the Riemann zeta function in the upper half-plane. We prove (on RH) that each of the inequalities G(x) < −0.02093 and G(x) > 0.02092 hold infinitely often, and establish improved bounds under an assumption of linearly independence for zeros of the zeta function. We also show that the bounds we obtain are very close to optimal.

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supporting

confidence: 59%

The size of oscillations in the Goldbach conjecture

Mossinghoff,

Trudgian

2020

Preprint

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“…In Chapter III, we revisit Landau's method and obtain measure theoretic results. Also we generalize a theorem of Kaczorowski and Szydło [24], and a theorem of Bhowmik, Ramaré and Schlage-Puchta [6] in Theorem 11.…”

Section: Frameworkmentioning

confidence: 83%

“…Theorem 10 (Bhowmik, Ramaré and Schlage-Puchta [6]). Suppose the conditions in Assumptions 2 hold, and let h(x) be as in Theorem 8.…”

Section: Measure Theoretic ω ± Resultsmentioning

confidence: 99%

“…In this chapter, we revisit a result due to Landau and obtain Ω ± results for ∆(x) using certain singularities of D(s). Also we shall measure the fluctuations of ∆(x) in terms of Ω bounds, which generalizes a result of Kaczorowski and Szydło [24], and a result of Bhowmik, Schlage-Puchta and Ramaré [6].…”

Section: Alternative Approchesmentioning

confidence: 94%

“…We shall show a quantitative version of Landau's theorem, which also generalizes a theorem of Gautami, Ramaré and Schlage-Puchta [6]. Below we state this theorem in a simplified way.…”

mentioning

confidence: 87%

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Measure-theoretic aspects of oscillations of error terms

Mahatab

Mukhopadhyay

2019

Acta Arith.

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Last, but not the least, I would like to thank my institute 'The Institute of Mathematical Sciences' for providing me a vibrant research environment. I have enjoyed excellent computer facility, a well managed library, clean and well furnished hostel and office rooms, and catering services at my institute. I would like to express my special gratitude to the library and administrative staffs of my institute for their efficient service.

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Oscillations in the Goldbach conjecture

Mossinghoff¹,

Trudgian²

2022

Journal De Théorie Des Nombres De Bordeaux

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Cet article est mis à disposition selon les termes de la licence CREATIVE COMMONS ATTRIBUTION -PAS DE MODIFICATION 4.0 FRANCE. http://creativecommons.org/licenses/by-nd/4.0/fr/ L'accès aux articles de la revue « Journal de Théorie des Nombres de Bordeaux » (http://jtnb.centre-mersenne.org/) implique l'accord avec les conditions générales d'utilisation (http://jtnb.centre-mersenne.org/legal/).

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Tauberian Oscillation Theorems and the Distribution of Goldbach numbers

Cited by 3 publications

References 5 publications

The size of oscillations in the Goldbach conjecture

The size of oscillations in the Goldbach conjecture

Measure-theoretic aspects of oscillations of error terms

Oscillations in the Goldbach conjecture

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