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Ld(1) IS O(logloglogd) FOR ALMOST ALL SQUARE FREE d

G. S. Mohan Reddy|SS Rau
장전수학회 (Jangjeon Mathematical Society)|2020.07|Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집) (Proceedings of the Jangjeon Mathematical Society)|제23권 제3호|pp. 341-345|DOI 10.17777/pjms.2020.23.3.006

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참고문헌

키워드

L-seriesDivisor functionsNormal orderHardy-Ramanujan estimate
주제분류수학

초록

Let d be a square free integer.Using Hardy-Ramanujan's value of nor- mal order of w(d) we show that Ld(1) = ○(logloglogd) except on a negligible set. We note that the proof verifies Robin's inequality σ(n) < eϒ nloglogn (equivalent form of Riemann Hypothesis) for such numbers.

Abstract

Let d be a square free integer.Using Hardy-Ramanujan's value of nor- mal order of w(d) we show that Ld(1) = ○(logloglogd) except on a negligible set. We note that the proof verifies Robin's inequality σ(n) < eϒ nloglogn (equivalent form of Riemann Hypothesis) for such numbers.

참고문헌 (19)

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  19. G Sudhaamsh, "An analogue 0f Landau-Walfisz Theorem", Accepted in AIP Conference Proceedings

관련 논문AI추천

PROOF OF THE MOBIUS CONJECTURE REVISITEDA. Bayad, M. GOUBI장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2013 · 제16권 제2호Ω-RESULT ON COEFFICIENTS OF AUTOMORPHIC L-FUNCTIONS OVER SPARSE SEQUENCESHongbin Wei, Huixue Lao대한수학회 · 대한수학회지2015 · 제52권 제5호ON AN ARITHMETIC INEQUALITY BY K. T. ATANASSOVJozsef Sandor, Lehel Kovacs장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2010 · 제13권 제3호Two arithmetic inequalitiesSandor장전수학회 · Advanced Studies in Contemporary Mathematics2010 · 제20권 제2호On Lehmer’s totient problem and its Unitary analogueC. Goverdhan, Hussain Abdulkader Al-Aidroos, V. Siva Rama Prasad장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2010 · 제13권 제2호Distribution of the values of the derivative of the Dirichlet L-functions at its a-pointsKamel Mazhouda, Mohamed Taib Jakhlouti대한수학회 · 대한수학회보2017 · 제54권 제4호

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