Results 21 to 30 of about 427 (155)
On sums of generalized Ramanujan sums [PDF]
Indian Journal of Pure and Applied Mathematics, 2015 Ramanujan sums have been studied and generalized by several authors. For example, Nowak studied these sums over quadratic number fields, and Grytczuk defined that on semigroups. In this note, we deduce some properties on sums of generalized Ramanujan sums and give examples on number fields.
openaire +2 more sources
Elliptic Dedekind-Rademacher Sums and Transformation Formulae of Certain Infinite Series [PDF]
, 2007 We give a transformation formula for certain infinite series in which some elliptic Dedekind-Rademacher sums arise. In the course of its proof, we also obtain a transformation formula for elliptic Dedekind-Rademacher sums. When a complex parameter $¥tau$
Machide, Tomoya
core +1 more source
On SA, CA, and GA numbers [PDF]
, 2012 Gronwall's function $G$ is defined for $n>1$ by $G(n)=\frac{\sigma(n)}{n \log\log n}$ where $\sigma(n)$ is the sum of the divisors of $n$. We call an integer $N>1$ a \emph{GA1 number} if $N$ is composite and $G(N) \ge G(N/p)$ for all prime factors $p$ of
Caveney, Geoffrey +2 more
core +3 more sources
An identity involving certain Hardy sums and Ramanujan’s sum [PDF]
Advances in Difference Equations, 2013 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Wang, Weiqiong, Han, Di
openaire +2 more sources
Asymptotics for rank and crank moments
, 2009 Moments of the partition rank and crank statistics have been studied for their connections to combinatorial objects such as Durfee symbols, as well as for their connections to harmonic Maass forms.
Bringmann, K., Mahlburg, K., Rhoades, R.
core +2 more sources
EXTENSIONS OF EULER-TYPE SUMS AND RAMANUJAN-TYPE SUMS
Kyushu Journal of Mathematics, 2021 We define a new kind of classical digamma function, and establish its some fundamental identities. Then we apply the formulas obtained, and extend tools developed by Flajolet and Salvy to study more general Euler type sums. The main results of Flajolet and Salvy's paper \cite{FS1998} are the immediate corollaries of main results in this paper ...
openaire +3 more sources
Moments of averages of generalized Ramanujan sums
, 2015 Let $\beta$ be a positive integer. A generalization of the Ramanujan sum due to Cohen is given by \begin{align} c_{q,\beta }(n) := \sum\limits_{{{(h,{q^\beta })}_\beta } = 1} {{e^{2\pi inh/{q^\beta }}}}, \nonumber \end{align} where $h$ ranges over the ...
Robles, Nicolas, Roy, Arindam
core +1 more source
An extension of Ramanujan’s sum
Duke Mathematical Journal, 1949 Verf. definiert eine Verallgemeinerung \(c_q^s(n)\) der Ramanujanschen Summe \(c_q(n)\) durch \(c_q^s(n) = \sum e^{2\pi inh/q^s}\), wobei \(n, q, s\) bestimmte natürliche Zahlen sind und die Summation über alle solchen nichtnegativen Werte von \(h\) zu erstrecken ist, die \(< q^s\) sind und keinen gemeinsamen Teiler \((\ne 1)\), der eine \(s\)-te ...
openaire +3 more sources
Differential regulation of translational stress responses by herpesvirus ubiquitin deconjugases
The FEBS Journal, EarlyView.Translating viral mRNAs is challenging due to structural features that may slow translation or induce ribosome stalling. The viral ubiquitin deconjugases encoded by human pathogenic herpesviruses regulate the cellular response to ribosomal stress by inhibiting various branches of the Ribosomal Quality Control (RQC) and activating Ribosomal Stress ...
Jiangnan Liu +3 more
wiley +1 more source
Artificial Intelligence in GeosciencesDenoising is an important preprocessing step in seismic exploration that improves the signal-to-noise ratio (SNR) and helps identify oil and minerals. Dictionary learning (DL) is a promising method for noise attenuation.
Lakshmi Kuruguntla +5 more
doaj +1 more source