Zero mode of the Fourier series of some modular graphs from Poincaré series
We consider specific linear combinations of two loop modular graph functions on the toroidal worldsheet with 2s links for s=2,3 and 4. In each case, it satisfies an eigenvalue equation with source terms involving E2s and Es2 only. On removing certain combinations of E2s and Es2 from it, we express t...
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| Format: | Article |
| Language: | English |
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Elsevier
2020-10-01
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| Series: | Physics Letters B |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S0370269320305189 |
| Summary: | We consider specific linear combinations of two loop modular graph functions on the toroidal worldsheet with 2s links for s=2,3 and 4. In each case, it satisfies an eigenvalue equation with source terms involving E2s and Es2 only. On removing certain combinations of E2s and Es2 from it, we express the resulting expression as an absolutely convergent Poincaré series. This is used to calculate the power behaved terms in the asymptotic expansion of the zero mode of the Fourier expansion of these graphs in a simple manner. |
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| ISSN: | 0370-2693 |