تقرير
Asymptotic identities for additive convolutions of sums of divisors
| العنوان: | Asymptotic identities for additive convolutions of sums of divisors |
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| المؤلفون: | Oliver, Robert J. Lemke, Shrestha, Sunrose T., Thorne, Frank |
| سنة النشر: | 2020 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Number Theory |
| الوصف: | In a 1916 paper, Ramanujan studied the additive convolution $S_{a, b}(n)$ of sum-of-divisors functions $\sigma_a(n)$ and $\sigma_b(n)$, and proved an asymptotic formula for it when $a$ and $b$ are positive odd integers. He also conjectured that his asymptotic formula should hold for all positive real $a$ and $b$. Ramanujan's conjecture was subsequently proved by Ingham, and then by Halberstam with a power saving error term. In this paper, we give a new proof of Ramanujan's conjecture that obtains lower order terms in the asymptotics for most ranges of the parameters. We also describe a connection to a counting problem in geometric topology that was studied in the second author's thesis and which served as our initial motivation in studying this sum. Comment: revised to rewrite the introduction, highlight main theorems and update references |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2007.09275 |
| رقم الأكسشن: | edsarx.2007.09275 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |