Bernoulli Identities and Combinatoric Convolution Sums with Odd Divisor Functions [PDF]
Abstract and Applied Analysis, 2014 We study the combinatoric convolution sums involving odd divisor functions, their relations to Bernoulli numbers, and some interesting applications.
Daeyeoul Kim, Yoon Kyung Park
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The spectral decomposition of shifted convolution sums [PDF]
, 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
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Euler Polynomials and Combinatoric Convolution Sums of Divisor Functions with Even Indices [PDF]
Abstract and Applied Analysis, 2014 We study combinatoric convolution sums of certain divisor functions involving even indices. We express them as a linear combination of divisor functions and Euler polynomials and obtain identities D2k(n)=(1/4)σ2k+1,0(n;2)-2·42kσ2k+1(n/4) -(1/2)[∑d|n,d ...
Daeyeoul Kim +2 more
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Weighted Sum of Correlated Lognormals: Convolution Integral Solution [PDF]
, 2011 Probability density function (pdf) for sum of n correlated lognormal variables is deducted as a special convolution integral. Pdf for weighted sums (where weights can be any real numbers) is also presented.
Nagy, Tamás
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Geometric Properties of Meromorphic Functions Involving Convolution Operator
Al-Mustansiriyah Journal of Science, 2022 We introduce and study a subclass of meromorphic univalent functions with positive coefficients defined by a novel operator and obtain coefficient estimates, closure theorems, convolution properties, partial sums, and δ- neighborhood for the class .
Ismael Ibrahim Hameed +1 more
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The multinomial convolution sum of a generalized divisor function
Open Mathematics, 2022 The main theorem of this article is to evaluate and express the multinomial convolution sum of the divisor function σr♯(n;N/4,N){\sigma }_{r}^{\sharp }\left(n;\hspace{0.33em}N\hspace{-0.08em}\text{/}\hspace{-0.08em}4,N) in as a simple form as possible ...
Park Ho
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On the Chebyshev polynomials and some of their new identities
Advances in Difference Equations, 2020 The main purpose of this paper is, using the elementary methods and properties of the power series, to study the computational problem of the convolution sums of Chebyshev polynomials and Fibonacci polynomials and to give some new and interesting ...
Di Han, Xingxing Lv
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Certain Class of Analytic Functions Connected with q-Analogue of the Bessel Function
Journal of Mathematics, 2021 The focus of this article is the introduction of a new subclass of analytic functions involving q-analogue of the Bessel function and obtained coefficient inequities, growth and distortion properties, radii of close-to-convexity, and starlikeness, as ...
Nazek Alessa +5 more
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Arithmetic convolution sums derived from eta quotients related to divisors of 6
Open Mathematics, 2022 The aim of this paper is to find arithmetic convolution sums of some restricted divisor functions. When divisors of a certain natural number satisfy a suitable condition for modulo 12, those restricted divisor functions are expressed by the coefficients ...
Ikikardes Nazli Yildiz +2 more
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On predictors for band-limited and high-frequency time series [PDF]
, 2012 Pathwise predictability and predictors for discrete time processes are studied in deterministic setting. It is suggested to approximate convolution sums over future times by convolution sums over past time. It is shown that all band-limited processes are
Dokuchaev +10 more
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