Results 1 to 9 of about 9 (9)
Large oscillations of the argument of the Riemann zeta‐function
Bulletin of the London Mathematical Society, Volume 53, Issue 6, Page 1776-1785, December 2021., 2021 Abstract Let S(t) denote the argument of the Riemann zeta‐function, defined as S(t)=1πImlogζ(1/2+it).Assuming the Riemann hypothesis, we prove that S(t)=Ω±logtlogloglogtloglogt.This improves the classical Ω‐results of Montgomery (Theorem 2; Comment. Math. Helv. 52 (1977) 511–518) and matches with the Ω‐result obtained by Bondarenko and Seip (Theorem 2;
Andrés Chirre, Kamalakshya Mahatab
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The first moment of primes in arithmetic progressions: beyond the Siegel–Walfisz range
Transactions of the London Mathematical Society, Volume 8, Issue 1, Page 174-185, December 2021., 2021 Abstract We investigate the first moment of primes in progressions ∑q⩽x/N(q,a)=1ψ(x;q,a)−xφ(q)as x,N→∞. We show unconditionally that, when a=1, there is a significant bias towards negative values, uniformly for N⩽eclogx. The proof combines recent results of the authors on the first moment and on the error term in the dispersion method.
Sary Drappeau, Daniel Fiorilli
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Linear correlations of multiplicative functions
Proceedings of the London Mathematical Society, Volume 121, Issue 2, Page 372-425, August 2020., 2020 Abstract We prove a Green–Tao type theorem for multiplicative functions.
Lilian Matthiesen
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Estimates of convolutions of certain number‐theoretic error terms
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 1, Page 1-23, 2004., 2004 Several estimates for the convolution function C [f(x)]:=∫1xf(y) f(x/y)(dy/y) and its iterates are obtained when f(x) is a suitable number‐theoretic error term. We deal with the case of the asymptotic formula for ∫0T|ζ(1/2+it)|2kdt(k = 1, 2), the general Dirichlet divisor problem, the problem of nonisomorphic Abelian groups of given order, and the ...
Aleksandar Ivić
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On a sum analogous to Dedekind sum and its mean square value formula
International Journal of Mathematics and Mathematical Sciences, Volume 32, Issue 1, Page 47-55, 2002., 2002 The main purpose of this paper is using the mean value theorem of Dirichlet L‐functions to study the asymptotic property of a sum analogous to Dedekind sum, and give an interesting mean square value formula.
Zhang Wenpeng
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Veterinary Dermatology, Volume 35, Issue 5, Page 500-507, October 2024.Abstract Background Canine atopic dermatitis (cAD) is a hereditary, generally pruritic and predominantly T‐cell‐driven inflammatory skin disease, involving an interplay between skin barrier abnormalities, allergen sensitisation and microbial dysbiosis.
L. Widorn +2 more
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Infant Mental Health Journal: Infancy and Early Childhood, Volume 45, Issue 5, Page 541-556, September 2024.Abstract An efficient, multidimensional instrument is needed to screen non‐optimal prenatal parental representations predictive of postnatal parenting behavior and child attachment. The present work aimed to revise and validate the Prenatal Caregiving Expectations Questionnaire—Revised (PCEQ‐R).
Katrine Røhder +5 more
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Veterinary Dermatology, Volume 35, Issue 4, Page 418-431, August 2024.Background – Diagnosis of canine adverse food reactions (AFRs) is based on vague criteria, such as ‘>50% improvement’ during elimination diet trial (EDT) followed by ‘deterioration’ during provocation test (PT). Objective – The objective of the study was to use predefined criteria to evaluate response during EDT [i.e., Owner Global Assessment of ...
Evi I. Sofou +4 more
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Arithmetic functions associated with infinitary divisors of an integer
, 1993 International Journal of Mathematics and Mathematical Sciences, Volume 16, Issue 2, Page 373-383, 1993.
Graeme L. Cohen, Peter Hagis
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