Eisenstein series and convolution sums
We compute Fourier series expansions of weight 2 and weight 4 Eisenstein series at various cusps. Then we use results of these computations to give formulas for the convolution sums ∑a+pb=nσ(a)σ(b), ∑p1a+p2b=nσ(a)σ(b) and ∑a+p1p2b=nσ(a)σ(b) where p,p1,p2 are primes.
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| Format: | Journal Article |
| Language: | English |
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2020
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| Online Access: | https://hdl.handle.net/10356/143048 |
| _version_ | 1826109948050800640 |
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| author | Aygin, Zafer Selcuk |
| author2 | School of Physical and Mathematical Sciences |
| author_facet | School of Physical and Mathematical Sciences Aygin, Zafer Selcuk |
| author_sort | Aygin, Zafer Selcuk |
| collection | NTU |
| description | We compute Fourier series expansions of weight 2 and weight 4 Eisenstein series at various cusps. Then we use results of these computations to give formulas for the convolution sums ∑a+pb=nσ(a)σ(b), ∑p1a+p2b=nσ(a)σ(b) and ∑a+p1p2b=nσ(a)σ(b) where p,p1,p2 are primes. |
| first_indexed | 2024-10-01T02:26:46Z |
| format | Journal Article |
| id | ntu-10356/143048 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T02:26:46Z |
| publishDate | 2020 |
| record_format | dspace |
| spelling | ntu-10356/1430482023-02-28T19:48:49Z Eisenstein series and convolution sums Aygin, Zafer Selcuk School of Physical and Mathematical Sciences Science::Mathematics Sum of Divisors Function Convolution Sums We compute Fourier series expansions of weight 2 and weight 4 Eisenstein series at various cusps. Then we use results of these computations to give formulas for the convolution sums ∑a+pb=nσ(a)σ(b), ∑p1a+p2b=nσ(a)σ(b) and ∑a+p1p2b=nσ(a)σ(b) where p,p1,p2 are primes. Ministry of Education (MOE) Accepted version This work was partially supported by the Singapore Ministry of Education Academic Research Fund, Tier2, Project Numbers MOE2014-T2-1-051, ARC40/14. 2020-07-23T04:29:00Z 2020-07-23T04:29:00Z 2018 Journal Article Aygin, Z. S. (2019). Eisenstein series and convolution sums. The Ramanujan Journal, 48(3), 495-508. doi:10.1007/s11139-018-0055-2 1382-4090 https://hdl.handle.net/10356/143048 10.1007/s11139-018-0055-2 2-s2.0-85054314619 3 48 495 508 en The Ramanujan Journal © 2018 Springer Science+Business Media, LLC, part of Springer Nature. This is a post-peer-review, pre-copyedit version of an article published in The Ramanujan Journal. The final authenticated version is available online at: http://dx.doi.org/10.1007/s11139-018-0055-2 application/pdf |
| spellingShingle | Science::Mathematics Sum of Divisors Function Convolution Sums Aygin, Zafer Selcuk Eisenstein series and convolution sums |
| title | Eisenstein series and convolution sums |
| title_full | Eisenstein series and convolution sums |
| title_fullStr | Eisenstein series and convolution sums |
| title_full_unstemmed | Eisenstein series and convolution sums |
| title_short | Eisenstein series and convolution sums |
| title_sort | eisenstein series and convolution sums |
| topic | Science::Mathematics Sum of Divisors Function Convolution Sums |
| url | https://hdl.handle.net/10356/143048 |
| work_keys_str_mv | AT ayginzaferselcuk eisensteinseriesandconvolutionsums |