- 【Updated on May 12, 2025】 Integration of CiNii Dissertations and CiNii Books into CiNii Research
- Trial version of CiNii Research Knowledge Graph Search feature is available on CiNii Labs
- Suspension and deletion of data provided by Nikkei BP
- Regarding the recording of “Research Data” and “Evidence Data”
An explicit construction of non-tempered cusp forms on $O(1,8n+1)$ (Analytic and Arithmetic Theory of Automorphic Forms)
-
- Li, Yingkun
- Fachbereich Mathematik, Technische Universität Darmstadt
-
- Narita, Hiro-aki
- Department of Mathematics, Faculty of Science and Engineering, Waseda University
-
- Pitale, Ameya
- Department of Mathematics, University of Oklahoma
Bibliographic Information
- Other Title
-
- An explicit construction of non-tempered cusp forms on O(1,8n+1)
Search this article
Description
This short note is a write-up of the results presented by the second named author at RIMS workshop "Analytic and arithmetic theory of automorphic forms" The main result is an explicit construction of the rcal analytic cusp forms on O ({imath}, 8n+1) by a lifting from Maass cusp forms of level one. The lifting is proved to be Hecke-equivariant. Our results include an explicit formula for Hecke eigenvalues of the lifts and explicit determination of the cusidal representations generated by them. This leads to showing the nontemperedness of the cuspidal representations at every finite place, namely our explicit construction provides "real analytic counterexamples to Ramanujan conjecture".
Journal
-
- RIMS Kokyuroku
-
RIMS Kokyuroku 2100 179-186, 2019-01
京都大学数理解析研究所
- Tweet
Details 詳細情報について
-
- CRID
- 1050566774764187520
-
- NII Article ID
- 120006861412
-
- NII Book ID
- AN00061013
-
- ISSN
- 18802818
-
- HANDLE
- 2433/251803
-
- NDL BIB ID
- 029628196
-
- Text Lang
- en
-
- Article Type
- departmental bulletin paper
-
- Data Source
-
- IRDB
- NDL Search
- CiNii Articles