Results 31 to 40 of about 683 (92)
On the mean square of the zeta-function and the divisor problem [PDF]
, 2006 Let $\Delta(x)$ denote the error term in the Dirichlet divisor problem, and $E(T)$ the error term in the asymptotic formula for the mean square of $|\zeta(1/2+it)|$. If $E^*(t) = E(t) - 2\pi\Delta^*(t/2\pi)$ with $\Delta^*(x) = -\Delta(x) + 2\Delta(2x) -
Aleksandar Ivić +4 more
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Counting $r$-tuples of positive integers with $k$-wise relatively prime components
, 2016 Let $r\ge k\ge 2$ be fixed positive integers. Let $\varrho_{r,k}$ denote the characteristic function of the set of $r$-tuples of positive integers with $k$-wise relatively prime components, that is any $k$ of them are relatively prime.
Tóth, László
core +1 more source
On the distribution of powered numbers
Open MathematicsAsymptotic formulae are established for the number of natural numbers mm with largest square-free divisor not exceeding mϑ{m}^{{\vartheta }}, for any fixed positive parameter ϑ{\vartheta }. Related counting functions are also considered.
Brüdern Jörg, Robert Olivier
doaj +1 more source
Partition regularity of Pythagorean pairs
Forum of Mathematics, PiWe address a core partition regularity problem in Ramsey theory by proving that every finite coloring of the positive integers contains monochromatic Pythagorean pairs (i.e., $x,y\in {\mathbb N}$ such that $x^2\pm y^2=z^2$ for some $z ...
Nikos Frantzikinakis +2 more
doaj +1 more source
On Primes Represented by Quadratic Polynomials
, 2007 This is a survey article on the Hardy-Littlewood conjecture about primes in quadratic progressions. We recount the history and quote some results approximating this hitherto unresolved conjecture.Comment: six(6) pages, minor changes were ...
Baier, Stephan, Zhao, Liangyi
core +5 more sources
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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Chebyshev's bias and generalized Riemann hypothesis [PDF]
, 2011 It is well known that $li(x)>\pi(x)$ (i) up to the (very large) Skewes' number $x_1 \sim 1.40 \times 10^{316}$ \cite{Bays00}. But, according to a Littlewood's theorem, there exist infinitely many $x$ that violate the inequality, due to the specific ...
Alamadhi, Adel +2 more
core +2 more sources
The search for non-symmetric ribbon knots
, 2019 We present the results of Axel Seeliger's tabulation of symmetric union presentations for ribbon knots with crossing numbers 11 and 12 and exhibit possible examples for ribbon knots which are not representable as symmetric unions.
Lamm, Christoph
core
Exponential and infinitary divisors [PDF]
, 2014 Our paper is devoted to several problems from the field of modified divisors: namely exponential and infinitary divisors. We study the behaviour of modified divisors, sum-of-divisors and totient functions.
Lelechenko, Andrew V.
core
Log-convexity and the overpartition function. [PDF]
Ramanujan J, 2023 Mukherjee G.
europepmc +1 more source