Multiple modular L-functions and modular iterated integrals
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866909020345860096 |
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| author | Yokomizo, Mahiro |
| author_facet | Yokomizo, Mahiro |
| contents | The connection between multiple modular L-functions, as defined by Manin in [5], and modular iterated integrals was made explicit by Choie and Ihara [3] under the restrictive assumption that all modular forms involved have vanishing constant terms in their q-expansions. In this paper, we remove the assumption and establish the relationship between modular iterated integrals and multiple modular L-functions for general modular forms, including those with nonzero constant terms. We also provide a proof of a functional equation for modular iterated integrals, which is a specialization of a general result obtained by Brown [2]. This leads us to a generalization of the result of Choie-Ihara [3]. In the final part of the paper, we compute explicit examples of modular iterated integrals. These calculations essentially reproduce the explicit initial computations carried out by Brown [2], but they also serve to validate the broader framework developed in this work. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_05672 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Multiple modular L-functions and modular iterated integrals Yokomizo, Mahiro Number Theory The connection between multiple modular L-functions, as defined by Manin in [5], and modular iterated integrals was made explicit by Choie and Ihara [3] under the restrictive assumption that all modular forms involved have vanishing constant terms in their q-expansions. In this paper, we remove the assumption and establish the relationship between modular iterated integrals and multiple modular L-functions for general modular forms, including those with nonzero constant terms. We also provide a proof of a functional equation for modular iterated integrals, which is a specialization of a general result obtained by Brown [2]. This leads us to a generalization of the result of Choie-Ihara [3]. In the final part of the paper, we compute explicit examples of modular iterated integrals. These calculations essentially reproduce the explicit initial computations carried out by Brown [2], but they also serve to validate the broader framework developed in this work. |
| title | Multiple modular L-functions and modular iterated integrals |
| topic | Number Theory |
| url | https://arxiv.org/abs/2605.05672 |