Abstract
The purpose of this note is to show how the theta-functions attached to certain indefinite quadratic forms of signature (2, 2) can be used to produce a map from certain spaces of cusp forms of Nebentype to Hilbert modular forms. The possibility of making such a construction was suggested by Niwa [4], and the techniques are the same as his and Shintani’s [6]. The construction of Hilbert modular forms from cusp forms of one variable has been discussed by many people, and I will not attempt to give a history of the subject here. However, the map produced by the theta-function is essentially the same as that of Doi and Naganuma [2], and Zagier [7]. In particular, the integral kernel Ω(τ, z1, z2) of Zagier is essentially the ‘holomorphic part’ of the theta-function.
Publisher
Cambridge University Press (CUP)
Reference12 articles.
1. Weil representation I. Intertwining distributions and discrete spectrum;Rallisg,1975
2. Indefinite quadratische formen und funktionentheorie I
3. On Modular Forms of Half Integral Weight
4. On construction of holomorphic cusp forms of half integral weight
5. Automorphic forms constructed from the Weil representation: holomorphic case;Rallisg,1976
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