Multiplicative Hecke operators and their applications
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866913578378854400 |
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| author | Kim, Chang Heon Shin, Gyucheol |
| author_facet | Kim, Chang Heon Shin, Gyucheol |
| contents | In this paper, we define the multiplicative Hecke operators $\mathcal{T}(n)$ for any positive integer on the integral weight meromorphic modular forms for $Γ_{0}(N)$. We then show that they have properties similar to those of additive Hecke operators. Moreover, we prove that multiplicative Hecke eigenforms with integer Fourier coefficients are eta quotients, and vice versa. In addition, we prove that the Borcherds product and logarithmic derivative are Hecke equivariant with the multiplicative Hecke operators and the Hecke operators on the half-integral weight harmonic weak Maass forms and weight 2 meromorphic modular forms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_01042 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Multiplicative Hecke operators and their applications Kim, Chang Heon Shin, Gyucheol Number Theory 11F03, 11F12, 11F20, 11F25, 11F37 In this paper, we define the multiplicative Hecke operators $\mathcal{T}(n)$ for any positive integer on the integral weight meromorphic modular forms for $Γ_{0}(N)$. We then show that they have properties similar to those of additive Hecke operators. Moreover, we prove that multiplicative Hecke eigenforms with integer Fourier coefficients are eta quotients, and vice versa. In addition, we prove that the Borcherds product and logarithmic derivative are Hecke equivariant with the multiplicative Hecke operators and the Hecke operators on the half-integral weight harmonic weak Maass forms and weight 2 meromorphic modular forms. |
| title | Multiplicative Hecke operators and their applications |
| topic | Number Theory 11F03, 11F12, 11F20, 11F25, 11F37 |
| url | https://arxiv.org/abs/2404.01042 |