On Variants of Inverse Cluster Size Problem & General Magnification
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866914360839897088 |
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| author | Jaiswal, Shubham Krithika, M Vanchinathan, P |
| author_facet | Jaiswal, Shubham Krithika, M Vanchinathan, P |
| contents | In this article we establish certain variants of the Inverse Cluster Size problem. We introduce the notion of primitive extensions and establish the Primitive variant of the problem. Precisely, we prove the existence of primitive extensions over number fields of any given degree and cluster size less than the degree. We also introduce the notions of Strong and Weak General Magnification and the notion of general primitive extensions. We establish some interesting cases of the General primitive variant of the problem. We also recall the notion of totally real number fields and resolve the Totally real variant of the problem completely. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_11841 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Variants of Inverse Cluster Size Problem & General Magnification Jaiswal, Shubham Krithika, M Vanchinathan, P Number Theory Group Theory 11R04, 11R21, 11R32, 12F05, 12F10, 20B35, 20F16 In this article we establish certain variants of the Inverse Cluster Size problem. We introduce the notion of primitive extensions and establish the Primitive variant of the problem. Precisely, we prove the existence of primitive extensions over number fields of any given degree and cluster size less than the degree. We also introduce the notions of Strong and Weak General Magnification and the notion of general primitive extensions. We establish some interesting cases of the General primitive variant of the problem. We also recall the notion of totally real number fields and resolve the Totally real variant of the problem completely. |
| title | On Variants of Inverse Cluster Size Problem & General Magnification |
| topic | Number Theory Group Theory 11R04, 11R21, 11R32, 12F05, 12F10, 20B35, 20F16 |
| url | https://arxiv.org/abs/2511.11841 |