Non-vanishing and sign changes of Hecke eigenvalues for Siegel cusp forms of genus two

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• 作者：Emmanuel Royer ; Jyoti Sengupta ; Jie Wu
• 关键词：Spinor zeta function ; Siegel form ; Fourier coefficients ; Hecke eigenvalues
• 刊名：The Ramanujan Journal
• 出版年：2016
• 出版时间：January 2016
• 年：2016
• 卷：39
• 期：1
• 页码：179-199
• 全文大小：504 KB
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• 作者单位：Emmanuel Royer (1)
  Jyoti Sengupta (2)
  Jie Wu (3)
  
  1. Laboratoire de Mathématiques, Université Blaise Pascal, Les Cézeaux, BP 80026, 63171, Aubière Cedex, France
  2. School of Mathematics, T.I.F.R., Homi Bhabha Road, Mumbai, 400 005, India
  3. Institut Élie Cartan de Lorraine, UMR 7502, Université de Lorraine, 54506, Vandœuvre-lès-Nancy, France
  
• 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

文摘

In this paper, we show that half of non-zero coefficients of the spinor zeta function of a Siegel cusp form of genus 2 are positive and half are negative. We also prove results concerning the non-vanishing in short intervals and strong cancellation among the coefficients evaluated at powers of a fixed prime. Our results rest on a Serre’s type density result established by Kowalski and Saha in the Appendix.