Multiple Dirichlet series and shifted convolutions

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• 作者：Jeff Hoffstein^a ; ^{jhoff@math.brown.edu" class="auth_mail" title="E-mail the corresponding author} ; Thomas A. Hulse^b ; ¹ ; ^{tahulse@colby.edu" class="auth_mail" title="E-mail the corresponding author} ; with appendix by Andre Reznikov^c ; ² ; ^{reznikov@math.biu.ac.il" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Subconvexity bounds ; Second moments ; Shifted convolutions ; L-functions of automorphic forms
• 刊名：Journal of Number Theory
• 出版年：2016
• 出版时间：April 2016
• 年：2016
• 卷：161
• 期：Complete
• 页码：457-533
• 全文大小：1066 K

文摘

We define, and obtain the meromorphic continuation of, shifted Rankin–Selberg convolutions in one and two variables. As sample applications, this continuation is used to obtain estimates for single and double shifted sums and a Burgess-type bound for L-series associated to modular forms of arbitrary central character. Further applications are furnished by subsequent works by the authors and their colleagues.