Identification of L-functions in the extended Selberg class by preimages of finite sets
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866915905330479104 |
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| author | Kundu, Arpita Banerjee, Abhijit |
| author_facet | Kundu, Arpita Banerjee, Abhijit |
| contents | In 2023, Li, Du, Yi proved a uniqueness theorem for L functions in the extended Selberg class under the assumptions of positive degree, a shared functional equation, and the sharing of three complex values. This was later strengthened by the present authors, who showed that sharing an arbitrary finite set of complex values, counted with multiplicities, still forces equality of the two L functions, again under the assumption that they satisfy the same functional equation. In this paper, we significantly improve all these results. We completely remove the requirement that the two L functions satisfy the same functional equation, yet we still obtain the same strong uniqueness conclusion under far weaker hypotheses. As a major consequence, we prove that every polynomial with distinct zeros is a strong uniqueness polynomial for L functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_00693 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Identification of L-functions in the extended Selberg class by preimages of finite sets Kundu, Arpita Banerjee, Abhijit Complex Variables In 2023, Li, Du, Yi proved a uniqueness theorem for L functions in the extended Selberg class under the assumptions of positive degree, a shared functional equation, and the sharing of three complex values. This was later strengthened by the present authors, who showed that sharing an arbitrary finite set of complex values, counted with multiplicities, still forces equality of the two L functions, again under the assumption that they satisfy the same functional equation. In this paper, we significantly improve all these results. We completely remove the requirement that the two L functions satisfy the same functional equation, yet we still obtain the same strong uniqueness conclusion under far weaker hypotheses. As a major consequence, we prove that every polynomial with distinct zeros is a strong uniqueness polynomial for L functions. |
| title | Identification of L-functions in the extended Selberg class by preimages of finite sets |
| topic | Complex Variables |
| url | https://arxiv.org/abs/2604.00693 |