On certain Gram matrices and their associated series
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910443908366336 |
|---|---|
| author | Ehm, Werner |
| author_facet | Ehm, Werner |
| contents | We derive formulae for Gram matrices arising in the Nyman--Beurling reformulation of the Riemann hypothesis. The development naturally leads upon series of the form $S(x) = \sum_{n\ge 1} R(nx)$ and their reciprocity relations. We give integral representations of these series; and we present decompositions of the quadratic forms associated with the Gram matrices along with a discussion of the components' properties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_06349 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On certain Gram matrices and their associated series Ehm, Werner Classical Analysis and ODEs Number Theory 30E20, 42A38 (Primary) 11M26 (Secondary) We derive formulae for Gram matrices arising in the Nyman--Beurling reformulation of the Riemann hypothesis. The development naturally leads upon series of the form $S(x) = \sum_{n\ge 1} R(nx)$ and their reciprocity relations. We give integral representations of these series; and we present decompositions of the quadratic forms associated with the Gram matrices along with a discussion of the components' properties. |
| title | On certain Gram matrices and their associated series |
| topic | Classical Analysis and ODEs Number Theory 30E20, 42A38 (Primary) 11M26 (Secondary) |
| url | https://arxiv.org/abs/2405.06349 |