All modular forms of weight 2 can be expressed by Eisenstein series
| Autor: | Jiacheng Xia, Martin Raum |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Cusp (singularity)
Pure mathematics Algebra and Number Theory Mathematics - Number Theory Mathematics::Number Theory 010102 general mathematics Modular form 01 natural sciences 010101 applied mathematics symbols.namesake Number theory Eisenstein series symbols FOS: Mathematics 11F11 11F67 11F25 Number Theory (math.NT) 0101 mathematics Linear combination Mathematics |
| DOI: | 10.48550/arxiv.1908.03616 |
| Popis: | We show that every elliptic modular form of integral weight greater than 1 can be expressed as linear combinations of products of at most two cusp expansions of Eisenstein series. This removes the obstruction of nonvanishing central $$\mathrm{L}$$ L -values present in all previous work. For weights greater than 2, we refine our result further, showing that linear combinations of products of exactly two cusp expansions of Eisenstein series suffice. |
| Databáze: | OpenAIRE |
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