Results 11 to 20 of about 625 (47)
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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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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Sums of products of Ramanujan sums [PDF]
, 2012 The Ramanujan sum $c_n(k)$ is defined as the sum of $k$-th powers of the primitive $n$-th roots of unity. We investigate arithmetic functions of $r$ variables defined as certain sums of the products $c_{m_1}(g_1(k))...c_{m_r}(g_r(k))$, where $g_1 ...
E. Cohen +12 more
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VALUE PATTERNS OF MULTIPLICATIVE FUNCTIONS AND RELATED SEQUENCES
Forum of Mathematics, Sigma, 2019 We study the existence of various sign and value patterns in sequences defined by multiplicative functions or related objects. For any set $A$ whose indicator function is ‘approximately multiplicative’ and uniformly distributed on short intervals in a ...
TERENCE TAO, JONI TERÄVÄINEN
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The Concordance Genus of 11--Crossing Knots
, 2013 The concordance genus of a knot is the least genus of any knot in its concordance class. It is bounded above by the genus of the knot, and bounded below by the slice genus, two well-studied invariants.
Kearney, M. Kate
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The least common multiple of a sequence of products of linear polynomials
, 2011 Let $f(x)$ be the product of several linear polynomials with integer coefficients. In this paper, we obtain the estimate: $\log {\rm lcm}(f(1), ..., f(n))\sim An$ as $n\rightarrow\infty $, where $A$ is a constant depending on $f$.Comment: To appear in ...
A. Selberg +12 more
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ON BINARY CORRELATIONS OF MULTIPLICATIVE FUNCTIONS
Forum of Mathematics, Sigma, 2018 We study logarithmically averaged binary correlations of bounded multiplicative functions $g_{1}$ and $g_{2}$ . A breakthrough on these correlations was made by Tao, who showed that the
JONI TERÄVÄINEN
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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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