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- Xia, Jiacheng,1991Chalmers tekniska högskola,Chalmers University of Technology (author)
Vector-valued Eisenstein series of congruence types and their products
- BookEnglish2019
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- Gothenburg,2019
- electronicrdacarrier
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- LIBRIS-ID:oai:research.chalmers.se:fd75c8d6-11ab-4d5b-8a60-f4ab87ccece7
- https://research.chalmers.se/publication/509882URI
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- Language:English
- Summary in:English
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- Historically, Kohnen and Zagier connected modular forms with period polynomials, and as a consequence of this association concluded that the products of at most two Eisenstein series span all spaces of classical modular forms of level 1. Later Borisov and Gunnells among other authors extended the result to higher levels. We consider this problem for vector-valued modular forms, establish the framework of congruence types and obtain the structure of the space of vector-valued Eisenstein series using tools from representation theory. Based on this development and historic results, we show that the space of vector-valued modular forms of certain weights and any congruence type can be spanned by the invariant vectors of that type tensor at most two Eisenstein series.
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- NATURVETENSKAP Matematik Algebra och logik hsv//swe
- NATURAL SCIENCES Mathematics Algebra and Logic hsv//eng
- NATURVETENSKAP Matematik hsv//swe
- NATURAL SCIENCES Mathematics hsv//eng
- NATURVETENSKAP Matematik Beräkningsmatematik hsv//swe
- NATURAL SCIENCES Mathematics Computational Mathematics hsv//eng
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- NATURAL SCIENCES Mathematics Geometry hsv//eng
- NATURVETENSKAP Matematik Diskret matematik hsv//swe
- NATURAL SCIENCES Mathematics Discrete Mathematics hsv//eng
- NATURVETENSKAP Matematik Matematisk analys hsv//swe
- NATURAL SCIENCES Mathematics Mathematical Analysis hsv//eng
- Hecke operator
- Fourier expansion of modular forms
- congruence type
- products of Eisenstein series
- vector-valued modular forms
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