Results 11 to 20 of about 52,800 (268)
Convolution identities for divisor sums and modular forms. [PDF]
Proc Natl Acad Sci U S AWe consider certain convolution sums that are the subject of a conjecture by Chester, Green, Pufu, Wang, and Wen in string theory. We prove a generalized form of their conjecture, explicitly evaluating absolutely convergent sums ∑
Fedosova K +2 more
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Eisenstein series and convolution sums [PDF]
The Ramanujan Journal, 2018 We compute Fourier series expansions of weight $2$ and weight $4$ Eisenstein series at various cusps. Then we use results of these computations to give formulas for the convolution sums $ \sum_{a+p b=n} (a) (b)$, $ \sum_{p_1a+p_2 b=n} (a) (b)$ and $ \sum_{a+p_1 p_2 b=n} (a) (b)$ where $p, p_1, p_2$ are primes.
Zafer Selcuk Aygin
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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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Evaluation of the convolution sums ∑al+bm=n lσ(l) σ(m) with ab ≤ 9
Open Mathematics, 2017 The generating functions of divisor functions are quasimodular forms of weight 2 and their products belong to a space of quasimodular forms of higher weight.
Park Yoon Kyung
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Transition mean values of shifted convolution sums
Journal of Number Theory, 2013 Let f be a classical holomorphic cusp form for SL_2(Z) of weight k which is a normalized eigenfunction for the Hecke algebra, and let (n) be its eigenvalues. In this paper we study "shifted convolution sums" of the eigenvalues (n) after averaging over many shifts h and obtain asymptotic estimates. The result is somewhat surprising: one encounters a
Ian Petrow
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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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CONVOLUTION SUMS INVOLVING THE DIVISOR FUNCTION [PDF]
Proceedings of the Edinburgh Mathematical Society, 2004 AbstractThe series\begin{alignat*}{2} L_{r,4}(q)\amp=\sum_{n=0}^\infty\sigma(4n+r)q^{4n+r},\amp\quad r\amp=0,1,2,3, \\ M_{r,4}(q)\amp=\sum_{n=0}^\infty\sigma_3(4n+r)q^{4n+r},\amp\quad r\amp=0,1,2,3, \\ N_{r,4}(q)\amp=\sum_{n=0}^\infty\sigma_5(4n+r)q^{4n+r},\amp\quad r\amp=0,1,2,3, \end{alignat*}are evaluated and used to prove convolution formulae such ...
Cheng, Nathalie, Williams, Kenneth S.
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