Results 1 to 10 of about 625 (47)
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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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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Odd values of the Klein j-function and the cubic partition function [PDF]
, 2015 In this note, using entirely algebraic or elementary methods, we determine a new asymptotic lower bound for the number of odd values of one of the most important modular functions in number theory, the Klein $j$-function.
Zanello, Fabrizio
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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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Another generalization of the gcd-sum function [PDF]
, 2013 We investigate an arithmetic function representing a generalization of the gcd-sum function, considered by Kurokawa and Ochiai in 2009 in connection with the multivariable global Igusa zeta function for a finite cyclic group.
Tóth, László
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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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Improving an inequality for the divisor function
, 2018 We improve using elementary means an explicit bound on the divisor function due to Friedlander and Iwaniec. Consequently we modestly improve a result regarding a sieving inequality for Gaussian sequences.Comment: 8 pages, to appear in Bull ...
Lay, Jeffrey P. S.
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