Deriving Discrete Convolution Sums Through Relationships With Ramanujan-Type Eisenstein Series

被引：0
|
作者：
Chandrashekara, Vidya Harekala [1 ]
Badanidiyoor, Ashwath Rao [2 ]
Bhat, Smitha Ganesh [1 ]
机构：
[1] Manipal Inst Technol, Manipal Acad Higher Educ, Dept Math, Manipal, Karnataka, India
[2] Manipal Inst Technol, Manipal Acad Higher Educ, Select Grade Dept Comp Sci, Manipal, Karnataka, India
来源：
ENGINEERING LETTERS | 2024年 / 32卷 / 07期
关键词：
convolution outcome; algebra; probability theory; numerical analysis; deep learning; CUBIC MODULAR IDENTITIES;
D O I：
暂无
中图分类号：
T [工业技术];
学科分类号：
08 ;
摘要：
This study seeks to establish connections between Ramanujan-type Eisenstein series and Borweins' cubic theta functions, employing the (p, k)-parametrization method introduced by Alaca. Furthermore, the derived identities are applied to provide a novel representation for the evaluation of the discrete convolution sum Sigma(2l+3m=n) delta(i)delta(j).
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收藏
页码：1500 / 1509
页数：10
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    [J]. The Ramanujan Journal, 2010, 23 : 17 - 44
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    Berndt, Bruce C.
    [J]. RAMANUJAN JOURNAL, 2010, 23 (1-3): : 17 - 44
  • [3] Eisenstein series and convolution sums
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    [J]. The Ramanujan Journal, 2019, 48 : 495 - 508
  • [4] Eisenstein series and convolution sums
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    [J]. RAMANUJAN JOURNAL, 2019, 48 (03): : 495 - 508
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    [J]. KYUSHU JOURNAL OF MATHEMATICS, 2021, 75 (02) : 295 - 322
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    [J]. CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES, 2024, 67 (02): : 350 - 368
  • [8] Error estimates of Ramanujan-type series
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    [J]. The Ramanujan Journal, 2012, 27 : 169 - 179
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