Results 11 to 20 of about 48,609 (140)

The average behaviour of a hybrid arithmetic function associated to cusp form coefficients over certain sparse sequence

Filomat, 2023
Let f be a normalized primitive holomorphic cusp form of even integral weight for the full modular group ? = SL(2,Z), and let ?f (n), ?(n) and ?(n) be the nth normalized Fourier coefficient of the cusp form f , the sum-of-divisors function and the ...
Guodong Hua
semanticscholar   +1 more source

Computing hypergeometric functions rigorously [PDF]

, 2016
We present an efficient implementation of hypergeometric functions in arbitrary-precision interval arithmetic. The functions ${}_0F_1$, ${}_1F_1$, ${}_2F_1$ and ${}_2F_0$ (or the Kummer $U$-function) are supported for unrestricted complex parameters and ...
Johansson, Fredrik
core   +5 more sources

Representation growth and representation zeta functions of groups [PDF]

, 2012
We give a short introduction to the subject of representation growth and representation zeta functions of groups, omitting all proofs. Our focus is on results which are relevant to the study of arithmetic groups in semisimple algebraic groups, such as ...
Klopsch, Benjamin
core   +3 more sources

The shifted convolution of generalized divisor functions [PDF]

, 2016
We prove an asymptotic formula for the shifted convolution of the divisor functions $d_k(n)$ and $d(n)$ with $k \geq 4$, which is uniform in the shift parameter and which has a power-saving error term, improving results obtained previously by Fouvry and ...
Topacogullari, Berke
core   +2 more sources

Phase singularities in complex arithmetic random waves [PDF]

Electronic Journal of Probability, 2016
Complex arithmetic random waves are stationary Gaussian complex-valued solutions of the Helmholtz equation on the two-dimensional flat torus. We use Wiener-It\^o chaotic expansions in order to derive a complete characterization of the second order high ...
F. Dalmao, I. Nourdin, G. Peccati, Maurizia Rossi   +3 more
semanticscholar   +1 more source

Chebyshev's bias for products of irreducible polynomials

, 2020
For any $k\geq 1$, this paper studies the number of polynomials having $k$ irreducible factors (counted with or without multiplicities) in $\mathbf{F}_q[t]$ among different arithmetic progressions.
Devin, Lucile, Meng, Xianchang
core   +3 more sources

The Zagier polynomials. Part II: Arithmetic properties of coefficients [PDF]

, 2013
The modified Bernoulli numbers \begin{equation*} B_{n}^{*} = \sum_{r=0}^{n} \binom{n+r}{2r} \frac{B_{r}}{n+r}, \quad n > 0 \end{equation*} introduced by D. Zagier in 1998 were recently extended to the polynomial case by replacing $B_{r}$ by the Bernoulli
Coffey, Mark W., De Angelis, Valerio, Dixit, Atul, Moll, Victor H., Straub, Armin, Vignat, Christophe   +5 more
core   +2 more sources

Asymptotic formulas for certain arithmetic functions

, 2008
This is an extended summary of a talk given by the last named author at the Czecho-Slovake Number Theory Conference 2005, held at Malenovice in September 2005.
M. Garaev, M. Kühleitner, Florian Luca, W. Nowak   +3 more
semanticscholar   +1 more source

Counting and effective rigidity in algebra and geometry

, 2018
The purpose of this article is to produce effective versions of some rigidity results in algebra and geometry. On the geometric side, we focus on the spectrum of primitive geodesic lengths (resp., complex lengths) for arithmetic hyperbolic 2-manifolds ...
A Borel, A Borel, A Lubotzky, A Lubotzky, A Lubotzky, A Macbeath, A Pethő, AM Odlyzko, AS Golsefidy, AW Reid, AW Reid, B Brindza, B Datskovsky, B Linowitz, B Linowitz, B Linowitz, B Linowitz, Benjamin Linowitz, C Maclachlan, C Maclachlan, C Millichap, C Millichap, D Futer, D Goldfeld, D Goldfeld, D. B. McReynolds, DA Marcus, DB McReynolds, DB McReynolds, E Artin, E Wirsing, G Prasad, GA Margulis, GA Margulis, GH Hardy, H Cohen, H Cohen, H Cohn, H Davenport, H Delange, H Delange, H Huber, I Reiner, J Neukirch, J Tits, J-P Serre, JC Lagarias, JS Meyer, JWS Cassels, K Takeuchi, L Hajdu, Lola Thompson, M Belolipetsky, M Belolipetsky, M Belolipetsky, M Bhargava, M Burger, M Larsen, M Liebeck, M-F Vignéras, MM Wood, MS Raghunathan, P Buser, Paul Pollack, R Gangolli, RS Pierce, S Brueggeman, S Lang, S Louboutin, S Wang, T Chinburg, T Chinburg, T Chinburg, T Chinburg, T Chinburg, T Gelander, T Gelander, T Sunada, TM Apostol, V Platonov, VI Chernousov, W Rudin, WP Thurston   +82 more
core   +1 more source

Vog: Using Volcanic Eruptions to Estimate the Health Costs of Particulates

The Economic Journal, EarlyView., 2018
The negative consequences of long‐term exposure to particulate pollution are well established but a number of studies find no effect of short‐term exposure on health outcomes. The high correlation of industrial pollutants complicates the estimation of the impact of individual pollutants on health.
Timothy J. Halliday, John Lynham, Áureo de Paula   +2 more
wiley   +1 more source