Results 21 to 30 of about 1,210,874 (307)
Integrated Partial Sums of Convolutions of Univalent Functions
Journal of Mathematical Analysis and Applications, 1993 AbstractLet S be the set of normalized univalent functions. We show that for f(z) = ∑∞k = 1akzk, g(z) = ∑∞k = 1bkzk ∈ S, [formula] if n < 3 or n > 6. For n = 4 we obtain the corresponding result if g is restricted to the class of close-to-convex functions.
Frode Rønning
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Shifted convolution sums involving theta series [PDF]
The Ramanujan Journal, 2017 Let $f$ be a cuspidal newform (holomorphic or Maass) of arbitrary level and nebentypus and denote by $ _f(n)$ its $n$-th Hecke eigenvalue. Let $$ r(n)=\#\left\{(n_1,n_2)\in \mathbb{Z}^2:n_1^2+n_2^2=n\right\}. $$ In this paper, we study the shifted convolution sum $$ \mathcal{S}_h(X)=\sum_{n\leq X} _f(n+h)r(n), \qquad 1\leq h\leq X, $$ and establish ...
Qingfeng Sun
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CERTAIN COMBINATORIAL CONVOLUTION SUMS INVOLVING DIVISOR FUNCTIONS PRODUCT FORMULA
, 2014 It is known that certain combinatorial convolution sums involving two divisor functions product formulae of arbitrary level can be explicitly expressed as a linear combination of divisor functions.
Daeyeoul Kim, Yoon Kyung Park
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Combinatorial convolution sums derived from divisor functions and Faulhaber sums
Glasnik Matematicki, 2014 It is known that certain convolution sums using Liouville identity can be expressed as a combination of divisor functions and Bernoulli numbers. In this article we find seven combinatorial convolution sums derived from divisor functions and Bernoulli ...
Ho Park, Daeyeoul Kim, Bumkyu Cho
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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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Finite Ramanujan expansions and shifted convolution sums of arithmetical functions, II [PDF]
, 2017 Giovanni Coppola, M. Ram Murty
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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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Evaluation of Convolution Sums entailing mixed Divisor Functions for a Class of Levels [PDF]
New Zealand Journal of Mathematics, 2019 Let $0< n,\alpha,\beta\in\mathbb{N}$ be such that $\gcd{(\alpha,\beta)}=1$. We carry out the evaluation of the convolution sums $\underset{\substack{ {(k,l)\in\mathbb{N}^{2}} \\ {\alpha\,k+\beta\,l=n} } }{\sum}\sigma(k)\sigma_{3}(l)$ and $\underset ...
Ebénézer Ntienjem
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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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Sums of multiplicative characters with additive convolutions [PDF]
Proceedings of the Steklov Institute of Mathematics, 2017 In the paper we obtain new estimates for binary and ternary sums of multiplicative characters with additive convolutions of characteristic functions of sets, having small additive doubling. In particular, we improve a result of M.-C. Chang. The proof uses Croot-Sisask almost periodicity lemma.
A. S. Volostnov, I. D. Shkredov
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