Results 41 to 50 of about 1,210,874 (307)
Evaluation of the convolution sum involving the sum of divisors function for 22, 44 and 52
Open Mathematics, 2017 The convolution sum, ∑(l,m)∈N02αl+βm=nσ(l)σ(m), $ \begin{array}{} \sum\limits_{{(l\, ,m)\in \mathbb{N}_{0}^{2}}\atop{\alpha \,l+\beta\, m=n}} \sigma(l)\sigma(m), \end{array} $ where αβ = 22, 44, 52, is evaluated for all natural numbers n. Modular forms
Ntienjem Ebénézer
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Q-Extension of Starlike Functions Subordinated with a Trigonometric Sine Function
Mathematics, 2020 The main purpose of this article is to examine the q-analog of starlike functions connected with a trigonometric sine function. Further, we discuss some interesting geometric properties, such as the well-known problems of Fekete-Szegö, the necessary and ...
Saeed Islam +4 more
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Subclasses of Noshiro-Type Starlike Harmonic Functions Involving q-Srivastava–Attiya Operator
Mathematics, 2023 In this paper, the harmonic function related to the q-Srivastava–Attiya operator is described to introduce a new class of complex harmonic functions that are orientation-preserving and univalent in the open-unit disk. We also cover some important aspects
Gangadharan Murugusundaramoorthy +3 more
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Non-Rectangular Convolutions and (Sub-)Cadences with Three Elements [PDF]
, 2019 The discrete acyclic convolution computes the 2n-1 sums sum_{i+j=k; (i,j) in [0,1,2,...,n-1]^2} (a_i b_j) in O(n log n) time. By using suitable offsets and setting some of the variables to zero, this method provides a tool to calculate all non-zero sums ...
Funakoshi, Mitsuru, Pape-Lange, Julian
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Estimates for character sums with various convolutions [PDF]
Acta Arithmetica, 2017 We provide estimates for sums of the form \[\left|\sum_{a\in A}\sum_{b\in B}\sum_{c\in C} (a+b+c)\right|\] and \[\left|\sum_{a\in A}\sum_{b\in B}\sum_{c\in C}\sum_{d\in D} (a+b+cd)\right|\] when $A,B,C,D\subset \mathbb F_p$, the field with $p$ elements and $ $ is a non-trivial multiplicative character modulo $p$.
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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
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IEEE Open Journal of the Solid-State Circuits Society, 2022 Due to the low-power priority of analog delay-based computation, time-domain computing-in-memory (TD-CIM) presents a splendid potential for energy-constrained edge and IoT scenarios deploying convolutional neural networks (CNNs).
Jianxun Yang +8 more
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On a shifted convolution sum problem
Journal of Number Theory, 2022 Abstract Let f be a holomorphic newform of prime level p and trivial nebentypus. For p 1 + e ≪ M ≪ p 3 − e , and 0 | u | ≪ M / p we prove that ∑ m = 1 ∞ λ f ( m ) λ f ( m + p u ) F ( m M ) ≪ p 1 / 4 + e M 3 / 4 where F is a ...
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A Convolution Approach on Partial Sums of Certain Harmonic Univalent Functions
International Journal of Mathematics and Mathematical Sciences, 2012 The purpose of the present paper is to establish some new results giving the sharp bounds of the real parts of ratios of harmonic univalent functions to their sequences of partial sums by using convolution.
Saurabh Porwal
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Some Upper Bounds for RKHS Approximation by Bessel Functions
Axioms, 2022 A reproducing kernel Hilbert space (RKHS) approximation problem arising from learning theory is investigated. Some K-functionals and moduli of smoothness with respect to RKHSs are defined with Fourier–Bessel series and Fourier–Bessel transforms ...
Mingdang Tian +2 more
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