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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sg-ntu-dr.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 |
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Science::Mathematics Sum of Divisors Function Convolution Sums |
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Science::Mathematics Sum of Divisors Function Convolution Sums Aygin, Zafer Selcuk Eisenstein series and convolution sums |
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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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School of Physical and Mathematical Sciences |
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School of Physical and Mathematical Sciences Aygin, Zafer Selcuk |
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Article |
| author |
Aygin, Zafer Selcuk |
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Aygin, Zafer Selcuk |
| title |
Eisenstein series and convolution sums |
| title_short |
Eisenstein series and convolution sums |
| title_full |
Eisenstein series and convolution sums |
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Eisenstein series and convolution sums |
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Eisenstein series and convolution sums |
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eisenstein series and convolution sums |
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2020 |
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https://hdl.handle.net/10356/143048 |
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