Some Density Results on Sets of Primes for Hecke Eigenvalues
Let f and g be two distinct holomorphic cusp forms for SL2ℤ, and we writeλfn and λgn for their corresponding Hecke eigenvalues. Firstly, we study the behavior of the signs of the sequences λfpλfpj for any even positive integer j. Moreover, we obtain the analytic density for the set of primes where t...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2021-01-01
|
| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/2462693 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832566448504963072 |
|---|---|
| author | Aiyue Zou Huixue Lao Shu Luo |
| author_facet | Aiyue Zou Huixue Lao Shu Luo |
| author_sort | Aiyue Zou |
| collection | DOAJ |
| description | Let f and g be two distinct holomorphic cusp forms for SL2ℤ, and we writeλfn and λgn for their corresponding Hecke eigenvalues. Firstly, we study the behavior of the signs of the sequences λfpλfpj for any even positive integer j. Moreover, we obtain the analytic density for the set of primes where the product λfpiλfpj is strictly less than λgpiλgpj. Finally, we investigate the distribution of linear combinations of λfpj and λgpj in a given interval. These results generalize previous ones. |
| format | Article |
| id | doaj-art-f2031b78d08b48eebcb259b6edfe01cc |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-f2031b78d08b48eebcb259b6edfe01cc2025-02-03T01:04:10ZengWileyJournal of Mathematics2314-46292314-47852021-01-01202110.1155/2021/24626932462693Some Density Results on Sets of Primes for Hecke EigenvaluesAiyue Zou0Huixue Lao1Shu Luo2School of Mathematics and Statistics, Shandong Normal University, Ji’nan, Shandong 250358, ChinaSchool of Mathematics and Statistics, Shandong Normal University, Ji’nan, Shandong 250358, ChinaSchool of Mathematics and Statistics, Shandong Normal University, Ji’nan, Shandong 250358, ChinaLet f and g be two distinct holomorphic cusp forms for SL2ℤ, and we writeλfn and λgn for their corresponding Hecke eigenvalues. Firstly, we study the behavior of the signs of the sequences λfpλfpj for any even positive integer j. Moreover, we obtain the analytic density for the set of primes where the product λfpiλfpj is strictly less than λgpiλgpj. Finally, we investigate the distribution of linear combinations of λfpj and λgpj in a given interval. These results generalize previous ones.http://dx.doi.org/10.1155/2021/2462693 |
| spellingShingle | Aiyue Zou Huixue Lao Shu Luo Some Density Results on Sets of Primes for Hecke Eigenvalues Journal of Mathematics |
| title | Some Density Results on Sets of Primes for Hecke Eigenvalues |
| title_full | Some Density Results on Sets of Primes for Hecke Eigenvalues |
| title_fullStr | Some Density Results on Sets of Primes for Hecke Eigenvalues |
| title_full_unstemmed | Some Density Results on Sets of Primes for Hecke Eigenvalues |
| title_short | Some Density Results on Sets of Primes for Hecke Eigenvalues |
| title_sort | some density results on sets of primes for hecke eigenvalues |
| url | http://dx.doi.org/10.1155/2021/2462693 |
| work_keys_str_mv | AT aiyuezou somedensityresultsonsetsofprimesforheckeeigenvalues AT huixuelao somedensityresultsonsetsofprimesforheckeeigenvalues AT shuluo somedensityresultsonsetsofprimesforheckeeigenvalues |