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arXiv · 1402.1854

Periods of modular forms and identities between Eisenstein series

Kamal Khuri-Makdisi·Wissam Raji
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Abstract

Borisov and Gunnells observed in 2001 that certain linear relations between products of two holomorphic weight 1 Eisenstein series had the same structure as the relations between periods of modular forms; a similar phenomenon exists in higher weights. We give a conceptual reason for this observation in arbitrary weight. This involves an unconventional way of expanding the Rankin-Selberg convolution of a cusp form with an Eisenstein series. We also prove a partial result towards understanding the action of a Hecke operator on a product of two Eisenstein series.

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Kamal Khuri-Makdisi, Wissam Raji. 2014-02-08. Periods of modular forms and identities between Eisenstein series. https://arxiv.org/abs/1402.1854

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