Results 21 to 30 of about 491,257 (81)
The existence of small prime gaps in subsets of the integers
, 2014 We consider the problem of finding small prime gaps in various sets of integers $\mathcal{C}$. Following the work of Goldston-Pintz-Yildirim, we will consider collections of natural numbers that are well-controlled in arithmetic progressions.
Benatar, Jacques
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Sharpenings of Li's criterion for the Riemann Hypothesis
, 2006 Exact and asymptotic formulae are displayed for the coefficients $\lambda_n$ used in Li's criterion for the Riemann Hypothesis. For $n \to \infty$ we obtain that if (and only if) the Hypothesis is true, $\lambda_n \sim n(A \log n +B)$ (with $A>0$ and $B$
A. Voros +15 more
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Abel Summation of Ramanujan-Fourier Series [PDF]
, 2015 Using Abel summation the paper proves a weak form of the Wiener-Khinchin formula for arithmetic functions with point-wise convergent Ramanujan-Fourier expansions.
Washburn, John
core
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
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Lucas' theorem: its generalizations, extensions and applications (1878--2014) [PDF]
, 2014 In 1878 \'E. Lucas proved a remarkable result which provides a simple way to compute the binomial coefficient ${n\choose m}$ modulo a prime $p$ in terms of the binomial coefficients of the base-$p$ digits of $n$ and $m$: {\it If $p$ is a prime, $n=n_0 ...
Meštrović, Romeo
core
On the Mahler measure of $1+X+1/X+Y+1/Y$
, 2011 We prove a conjectured formula relating the Mahler measure of the Laurent polynomial $1+X+X^{-1}+Y+Y^{-1}$, to the $L$-series of a conductor 15 elliptic curve.Comment: 18 pages, Fixed typos in Lemmas 3 and
Berndt +22 more
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Overpseudoprimes, and Mersenne and Fermat numbers as primover numbers [PDF]
, 2012 We introduce a new class of pseudoprimes-so called "overpseudoprimes to base $b$", which is a subclass of strong pseudoprimes to base $b$. Denoting via $|b|_n$ the multiplicative order of $b$ modulo $n$, we show that a composite $n$ is overpseudoprime if
Castillo, John H. +3 more
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An Ap\'ery-like difference equation for Catalan's constant
, 2002 Applying Zeilberger's algorithm of creative telescoping to a family of certain very-well-poised hypergeometric series involving linear forms in Catalan's constant with rational coefficients, we obtain a second-order difference equation for these forms ...
Zudilin, Wadim
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A classical introduction to modern number theory
Graduate texts in mathematics, 1982 K. Ireland, M. Rosen
semanticscholar +1 more source
Algebraic Number Theory and Code Design for Rayleigh Fading Channels
Foundations and Trends in Communications and Information Theory, 2004 F. Oggier, E. Viterbo
semanticscholar +1 more source