Shifted convolution of cusp-forms with \(\theta \) -series

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• 作者：Guangshi Lü ; Jie Wu ; Wenguang Zhai
• 刊名：The Ramanujan Journal
• 出版年：2016
• 出版时间：May 2016
• 年：2016
• 卷：40
• 期：1
• 页码：115-133
• 全文大小：496 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Number Theory
  Field Theory and Polynomials
  Combinatorics
  Fourier Analysis
  Functions of a Complex Variable
  
• 出版者：Springer U.S.
• ISSN：1572-9303
• 卷排序：40

文摘

In this paper we apply some simple approaches to improve a recent result of Luo on the shifted convolution sum of the Fourier coefficients of a cusp form and a theta series. A mean square formula is established in order to explore the right order of magnitude of this shifted convolution sum.KeywordShifted convolution, Cusp form, Theta series