Theta-functions and Hilbert modular forms
نویسندگان
چکیده
منابع مشابه
Hilbert modular forms of weight 1/2 and theta functions
Serre and Stark found a basis for the space of modular forms of weight 1/2 in terms of theta series. In this paper, we generalize their result under certain mild restrictions on the level and character to the case of weight 1/2 Hilbert modular forms over a totally real field of narrow class number 1. The methods broadly follow those of Serre-Stark; however we are forced to overcome technical di...
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Ramanujan’s last letter to Hardy concerns the asymptotic properties of modular forms and his ‘mock theta functions’. For the mock theta function f (q), Ramanujan claims that as q approaches an even-order 2k root of unity, we have f (q)− (−1)(1− q)(1− q)(1− q) · · · (1− 2q+ 2q − · · ·)= O(1). We prove Ramanujan’s claim as a special case of a more general result. The implied constants in Ramanuja...
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ژورنال
عنوان ژورنال: Nagoya Mathematical Journal
سال: 1978
ISSN: 0027-7630,2152-6842
DOI: 10.1017/s0027763000017955