Results 1 to 10 of about 683 (92)
The first moment of primes in arithmetic progressions: beyond the Siegel–Walfisz range
Transactions of the London Mathematical Society, 2021 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.
Sary Drappeau, Daniel Fiorilli
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Squarefree Integers in Arithmetic Progressions to Smooth Moduli
Forum of Mathematics, Sigma, 2021 Let $\varepsilon> 0$ be sufficiently small and let $0 < \eta < 1/522$ . We show that if X is large enough in terms of $\varepsilon $ , then for any squarefree integer $q \leq X^{196/261-\varepsilon }$ that is $X^{\eta ...
Alexander P. Mangerel
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On the Restricted Divisor Function in Arithmetic Progressions [PDF]
, 2010 We obtain several asymptotic estimates for the sums of the restricted divisor function τM,N (k) = #{1 6 m 6 M, 1 6 n 6 N : mn = k} over short arithmetic progressions, which improve some results of J. Truelsen.
I. Shparlinski
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THE LOGARITHMICALLY AVERAGED CHOWLA AND ELLIOTT CONJECTURES FOR TWO-POINT CORRELATIONS
Forum of Mathematics, Pi, 2016 Let $\unicode[STIX]{x1D706}$ denote the Liouville function. The Chowla conjecture, in the two-point correlation case, asserts that
TERENCE TAO
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On the k-free divisor problem (II) [PDF]
, 2008 2000 Mathematics Subject Classi cation: Primary 11N37.Key words and phrases: Dirichlet divisor problem, k-free divisor problem.J. Furuya is supported by a Grant-in-Aid for Scienti c Research from the Ministry ofEducation, Science, Sports and Culture ...
J. Furuya, W. Zhai
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Forum of Mathematics, Pi, 2020 We determine the order of magnitude of $\mathbb{E}|\sum _{n\leqslant x}f(n)|^{2q}$, where $f(n)$ is a Steinhaus or Rademacher random multiplicative function, and $0\leqslant q\leqslant 1$.
ADAM J. HARPER
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Iteration of Composition Operators on small Bergman spaces of Dirichlet series
Concrete Operators, 2018 The Hilbert spaces ℋw consisiting of Dirichlet series F(s)=∑n=1∞ann-s$F(s) = \sum\nolimits_{n = 1}^\infty {{a_n}{n^{ - s}}}$ that satisfty ∑n=1∞|an|2/wn 0 and {wn}n having average order (logj+n)α${(\log _j^ + n)^\alpha }$, that the composition operators ...
Zhao Jing
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SIGN PATTERNS OF THE LIOUVILLE AND MÖBIUS FUNCTIONS
Forum of Mathematics, Sigma, 2016 Let ${\it\lambda}$ and ${\it\mu}$ denote the Liouville and
KAISA MATOMÄKI +2 more
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SECOND MOMENTS IN THE GENERALIZED GAUSS CIRCLE PROBLEM
Forum of Mathematics, Sigma, 2018 The generalized Gauss circle problem concerns the lattice point discrepancy of large spheres. We study the Dirichlet series associated to $P_{k}(n)^{2}$, where $P_{k}(n)$ is the discrepancy between the volume of the $k$-dimensional sphere of radius ...
THOMAS A. HULSE +3 more
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Publicationes mathematicae (Debrecen), 1997 . We introduce the notion of cross-convolution of arithmetical functions as a special case of Narkiewicz’s regular convolution. We give asymptotic formulae for the summatory functions of certain generalized divisor-sum functions and Euler-type functions ...
L. Tóth
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