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Weights of Modular Forms on so + (2, l ) and Congruences Between Eisenstein Series and Cusp forms of Half‐Integral Weight on SL 2
Author(s) -
Hill Richard
Publication year - 2007
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s0025579300000206
Subject(s) - mathematics , eisenstein series , modular form , cusp (singularity) , congruence relation , modulo , cusp form , pure mathematics , series (stratigraphy) , mathematical analysis , combinatorics , geometry , paleontology , biology
Let E be a level 1, vector valued Eisenstein series of half‐integral weight, normalized so that the coefficients are all in ℤ. It is shown that there is a level one vector valued cusp form f with the same weight as E and with coefficients in ℤ, which is congruent to E modulo the constant term of E .
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