标题:Sums of Fourier coefficients of cusp forms of level D twisted by exponential functions
作者:Liu, Huan
作者机构:[Liu, H] School of Mathematics, Shandong University, Jinan, 250100, China
通讯作者:Liu, H(liuhuansdu@hotmail.com)
通讯作者地址:[Liu, H]Shandong Univ, Sch Math, Jinan 250100, Peoples R China.
来源:中国数学前沿
出版年:2017
卷:12
期:3
页码:655-673
DOI:10.1007/s11464-016-0534-y
关键词:exponential sums;cusp form;Fourier coefficients
摘要:Let g be a holomorphic or Maass Hecke newform of level D and nebentypus xD,and let ag(n) be its n-th Fourier coefficient.We consider the sum S1 =∑-X<n≤2xag(n)e(αnβ) and prove that S1 has an asymptotic formula when β =1/2 and α is close to ±2√q/D for positive integer q ≤ X/4 and X sufficiently large.And when 0 < β < 1 and α,β fail to meet the above condition,we obtain upper bounds of S1.We also consider the sum S2 =∑n>0 ag(n)e(αnβ)φ(n/X) with φ(x) ∈ C∞c(0,+∞) and prove that S2 has better upper bounds than S1 at some special α andβ.
收录类别:CSCD;SCOPUS;SCIE
WOS核心被引频次:1
Scopus被引频次:1
资源类型:期刊论文
原文链接:https://www.scopus.com/inward/record.uri?eid=2-s2.0-84975132670&doi=10.1007%2fs11464-016-0534-y&partnerID=40&md5=e6eb201695ee86217b16aa8b82a87c21
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