Journal article
Double first moment for L(12,Sym2f×g) by applying Petersson's formula twice
Journal of number theory, Vol.202, pp.141-159
09/2019
DOI: 10.1016/j.jnt.2019.01.014
Abstract
For holomorphic cusp forms f of weight k1 and g of weight k2 for SL(2,Z), bounds are proved for sums of L(12,Sym2f×g) over both f and g. Since these central values are known to be non-negative, the Lindelöf Hypothesis on average for both f and g follows. As a consequence, bounds for sums of the central values over g are proved for any f with its weight k1 tending to ∞ in certain ways. Subconvexity bounds for individual central values are also established in the two weight aspects for all f and all but a relatively small number of exceptional g. As an application, subconvexity bounds for the triple product L-function L(s,f×f×g) are also established. These subconvexity bounds for non-exceptional g's allow f to move and exceed the strength of all known bounds and the Weyl-type bound.
Details
- Title: Subtitle
- Double first moment for L(12,Sym2f×g) by applying Petersson's formula twice
- Creators
- Haiwei Sun - School of Mathematics and Statistics, Shandong University, Weihai, Shandong 264209, ChinaYangbo Ye - Department of Mathematics, The University of Iowa, Iowa City, IA 52242-1419, USA
- Resource Type
- Journal article
- Publication Details
- Journal of number theory, Vol.202, pp.141-159
- DOI
- 10.1016/j.jnt.2019.01.014
- ISSN
- 0022-314X
- eISSN
- 1096-1658
- Publisher
- Elsevier Inc
- Grant note
- DOI: 10.13039/501100004543, name: China Scholarship Council, award: 201706225004; DOI: 10.13039/501100001809, name: National Natural Science Foundation of China, award: 11601271; DOI: 10.13039/501100002858, name: China Postdoctoral Science Foundation, award: 2016M602125
- Language
- English
- Date published
- 09/2019
- Academic Unit
- Mathematics
- Record Identifier
- 9983985883902771
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