Article
| Title: | On the distribution of the sequence of integers $d(n^2)$ (English) |
| Author: | Kampamolla, Venkatasubbareddy |
| Author: | Ayyadurai, Sankaranarayanan |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 76 |
| Issue: | 2 |
| Year: | 2026 |
| Pages: | 515-524 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | We study the distribution of the sequence of integers $d(n^2)$ under the assumption of the strong Riemann hypothesis. Under this assumption, we provide a refined asymptotic formula for the sum $${\sum _{n\leq x}}d(n^2)$$ with an improved error term by extracting some more main terms. (English) |
| Keyword: | Dirichlet series |
| Keyword: | Riemann zeta function |
| Keyword: | Riemann hypothesis |
| Keyword: | Perron formula |
| MSC: | 11M06 |
| MSC: | 11M26 |
| DOI: | 10.21136/CMJ.2026.0310-25 |
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| Date available: | 2026-05-22T11:20:42Z |
| Last updated: | 2026-05-25 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/153646 |
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| Reference: | [8] Ramachandra, K., Sankaranarayanan, A.: On an asymptotic formula of Srinivasa Ramanujan.Acta Arith. 109 (2003), 349-357. Zbl 1036.11045, MR 2009049, 10.4064/aa109-4-5 |
| Reference: | [9] Titchmarsh, E. C.: The Theory of the Riemann Zeta-Function.Clarendon Press, Oxford (1986). Zbl 0601.10026, MR 0882550 |
| Reference: | [10] Venkatasubbareddy, K., Sankaranarayanan, A.: On the distribution of the strongly multiplicative function $2^{\omega(n)}$ on the set of natural numbers.Available at https://arxiv.org/abs/2502.02598 (2025), 16 pages. 10.48550/arXiv.2502.02598 |
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