Cyclic Vanishing Identities of Sun-Pan Type: Analytic and Modular Perspectives
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915530485530624 |
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| author | Nagai, Ken |
| author_facet | Nagai, Ken |
| contents | We revisit the cyclic identities of Sun--Pan type for Bernoulli polynomials and their $q$-analogues. From the analytic side, we formulate minimal Appell axioms that force cyclic vanishing identities, extending naturally to $q$-Appell sequences and analytic Bernoulli functions. From the modular side, we show that the same relations arise as period polynomial identities associated with Eisenstein series, reflecting the symmetry $(ST)^3=-I$ of the modular group. These two complementary perspectives place the Sun--Pan cyclic identities at the crossroads of number theory, special functions, and modular forms, and suggest further connections to polylogarithms, $L$-values, and mixed Tate motives. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_01341 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Cyclic Vanishing Identities of Sun-Pan Type: Analytic and Modular Perspectives Nagai, Ken General Mathematics 11B68 (Primary), 11M06, 11F11 (Secondary) We revisit the cyclic identities of Sun--Pan type for Bernoulli polynomials and their $q$-analogues. From the analytic side, we formulate minimal Appell axioms that force cyclic vanishing identities, extending naturally to $q$-Appell sequences and analytic Bernoulli functions. From the modular side, we show that the same relations arise as period polynomial identities associated with Eisenstein series, reflecting the symmetry $(ST)^3=-I$ of the modular group. These two complementary perspectives place the Sun--Pan cyclic identities at the crossroads of number theory, special functions, and modular forms, and suggest further connections to polylogarithms, $L$-values, and mixed Tate motives. |
| title | Cyclic Vanishing Identities of Sun-Pan Type: Analytic and Modular Perspectives |
| topic | General Mathematics 11B68 (Primary), 11M06, 11F11 (Secondary) |
| url | https://arxiv.org/abs/2510.01341 |