Results 41 to 50 of about 52,800 (268)

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

A Note on the Tail Behavior of Randomly Weighted Sums with Convolution-Equivalently Distributed Random Variables

Abstract and Applied Analysis, 2013
We investigate the tailed asymptotic behavior of the randomly weighted sums with increments with convolution-equivalent distributions. Our obtained result can be directly applied to a discrete-time insurance risk model with insurance and financial risks ...
Yang Yang, Jun-feng Liu, Yu-lin Zhang
doaj   +1 more source

On the Relation Between Fourier Frequency and Period for Discrete Signals, and Series of Discrete Periodic Complex Exponentials

IEEE Open Journal of Signal Processing, 2021
Discrete complex exponentials are almost periodic signals, not always periodic; when periodic, the frequency determines the period, but not viceversa, the period being a chaotic function of the frequency, expressible in terms of Thomae's function.
Alfredo Restrepo, Julian Quiroga, Jairo Hurtado   +2 more
doaj   +1 more source

New Subclasses of Multivalent Analytic Functions Associated with a Linear Operator

Abstract and Applied Analysis, 2013
Making use of a linear operator, which is defined here by means of the Hadamard product (or convolution), we consider two subclasses and of multivalent analytic functions with negative coefficients in the open unit disk. Some modified Hadamard products,
Ding-Gong Yang, Jin-Lin Liu
doaj   +1 more source

Some Types of Identities Involving the Legendre Polynomials

Mathematics, 2019
In this paper, a new non-linear recursive sequence is firstly introduced. Then, using this sequence, a computational problem involving the convolution of the Legendre polynomial is studied using the basic and combinatorial methods.
Shimeng Shen, Li Chen
doaj   +1 more source

Pascu-Rønning Type Meromorphic Functions Based on Sălăgean-Erdély–Kober Operator

Axioms, 2023
In the present investigation, we introduce a new class of meromorphic functions defined in the punctured unit disk Δ*:={ϑ∈C ...
Sheza M. El-Deeb, Gangadharan Murugusundaramoorthy, Kaliappan Vijaya, Alhanouf Alburaikan   +3 more
doaj   +1 more source

Bernoulli Polynomials and Convolution Sums [PDF]

British Journal of Mathematics & Computer Science, 2014
In this paper, we study the summations ∑ (a,b,c)∈N a+b+c=n (f(a+ b) + f(b+ c) + f(c+ a)) and ∑ (a,b,c,d)∈N a+b+c+d=n (f(a+ b+ c) + f(b+ c+ d) + f(c+ d+ a)). Especially, for the first summation we obtain some relations related to Bernoulli and Euler polynomials.
openaire   +1 more source

Differentiation of the Mittag-Leffler Functions with Respect to Parameters in the Laplace Transform Approach

Mathematics, 2020
In this work, properties of one- or two-parameter Mittag-Leffler functions are derived using the Laplace transform approach. It is demonstrated that manipulations with the pair direct–inverse transform makes it far more easy than previous methods to ...
Alexander Apelblat
doaj   +1 more source

The spectral decomposition of shifted convolution sums

, 2007
We obtain a spectral decomposition of shifted convolution sums in Hecke eigenvalues of holomorphic or Maass cusp forms.Comment: 15 pages, LaTeX2e; v2: corrected and slightly expanded ...
Blomer, Valentin, Harcos, Gergely
core   +1 more source

CONVOLUTION SUM OF RAMANUJAN'S SUM

, 2022
This article is the result of calculating the convolution of Ramanujan's sum and natural number multiplied. Among these results, special values are expressed by Euler and Bernoulli functions.
Hwan Jo, Gye, Bayad, Abdelmejid, Kim, Daeyeoul   +2 more
openaire   +2 more sources