Riesz-type criteria and theta transformation analogues

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• 作者：Atul Dixit^a ; ^b ; ^{adixit@tulane.edu" class="auth_mail" title="E-mail the corresponding author} ; ^{adixit@iitgn.ac.in" class="auth_mail" title="E-mail the corresponding author} ; Arindam Roy^c ; ^{roy22@illinois.edu" class="auth_mail" title="E-mail the corresponding author} ; Alexandru Zaharescu^c ; ^d ; ^{zaharesc@math.uiuc.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：primary ; 11M06 ; secondary ; 11M26 ; 33C15
• 刊名：Journal of Number Theory
• 出版年：2016
• 出版时间：March 2016
• 年：2016
• 卷：160
• 期：Complete
• 页码：385-408
• 全文大小：415 K

文摘

We give character analogues of a generalization of a result due to Ramanujan, Hardy and Littlewood, and provide Riesz-type criteria for Riemann Hypotheses for the Riemann zeta function and Dirichlet L-functions. We also provide analogues of the general theta transformation formula and of recent generalizations of the transformation formulas of W.L. Ferrar and G.H. Hardy for real primitive Dirichlet characters.