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• W3098642236 abstract "Let k be an odd integer ≥ 3 and N be a positive integer such that 4|N. Let χ be an even Dirichlet character modulo N. Shimura decomposes the space of half-integral weight cusp forms S k/2 (N,χ) as a direct sum [Formula: see text] where F runs through all newforms of weight k - 1, level dividing N/2 and character χ 2 , the space S k/2 (N,χ,F) is the subspace of forms that are Shimura equivalent to F, and the space S 0 (N,χ) is the subspace spanned by single-variable theta-series. The explicit computation of this decomposition is important for practical applications of a theorem of Waldspurger relating the critical values of L-functions of quadratic twists of newforms of even integral weight to coefficients of modular forms of half-integral weight. In this paper, we give a more precise definition of the summands S k/2 (N,χ,F) whilst proving that it is equivalent to Shimura's definition. We use our definition to give a practical algorithm for computing Shimura's decomposition, and illustrate this with some examples." @default.
• W3098642236 created "2020-11-23" @default.
• W3098642236 creator A5026377197 @default.
• W3098642236 date "2013-09-01" @default.
• W3098642236 modified "2023-10-18" @default.
• W3098642236 title "ON SHIMURA'S DECOMPOSITION" @default.
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• W3098642236 doi "https://doi.org/10.1142/s179304211350036x" @default.
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