Results 11 to 20 of about 947,467 (42)

Smooth numbers in Beatty sequences [PDF]

arXiv, 2021
An asymptotic formula is given for the number of y-smooth numbers up to x in a Beatty sequence corresponding to an irrational number of finite type.
arxiv  

Discretisation for odd quadratic twists [PDF]

, 2005
The discretisation problem for even quadratic twists is almost understood, with the main question now being how the arithmetic Delaunay heuristic interacts with the analytic random matrix theory prediction.
Conrey, J. Brian, Rubinstein, Michael O., Snaith, Nina C., Watkins, Mark   +3 more
core   +3 more sources

New harmonic number identities with applications [PDF]

, 2009
We determine the explicit formulas for the sum of products of homogeneous multiple harmonic sums $\sum_{k=1}^n \prod_{j=1}^r H_k(\{1\}^{\lambda_j})$ when $\sum_{j=1}^r \lambda_j\leq 5$.
Tauraso, Roberto
core   +3 more sources

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  

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, André Voros, C. J. Vallée-Poussin de la, D. H. Lehmer, E. Bombieri, J. B. Keiper, M. I. Israilov, M. W. Coffey, N. Kurokawa, P. Biane, R. B Dingle, X.-J. Li, X.-J. Li, X.-J. Li, Y. Hashimoto, Y. Matsuoka   +15 more
core   +1 more source

Enumerative Galois theory for number fields [PDF]

arXiv, 2023
Recently Bhargava counted number fields with prescribed Galois group. We improve the bound in four specific cases.
arxiv  

Laurent Polynomials and Superintegrable Maps [PDF]

, 2007
This article is dedicated to the memory of Vadim Kuznetsov, and begins with some of the author's recollections of him. Thereafter, a brief review of Somos sequences is provided, with particular focus being made on the integrable structure of Somos-4 ...
Hone, Andrew N.W.
core  

Distribution of Farey Fractions in Residue Classes and Lang--Trotter Conjectures on Average

, 2007
We prove that the set of Farey fractions of order $T$, that is, the set $\{\alpha/\beta \in \Q : \gcd(\alpha, \beta) = 1, 1 \le \alpha, \beta \le T\}$, is uniformly distributed in residue classes modulo a prime $p$ provided $T \ge p^{1/2 +\eps}$ for any ...
Cojocaru, A. C., Shparlinski, I. E.
core   +1 more source

Rank distribution in a family of cubic twists [PDF]

, 2005
In 1987, Zagier and Kramarz published a paper in which they presented evidence that a positive proportion of the even-signed cubic twists of the elliptic curve $x^3+y^3=1$ should have positive rank.
Watkins, Mark
core   +2 more sources

Invitation to higher local fields (Introduction) [PDF]

Geom. Topol. Monogr. Volume 3(2000) iii-xi, 2000
The monograph "Invitation to higher local fields" is the result of the conference on higher local fields held in Muenster, August 29 to September 5, 1999. The aim is to provide an introduction to higher local fields (more generally complete discrete valuation fields with arbitrary residue field) and render the main ideas of this theory (Part I), as ...
arxiv