当前位置: X-MOL 学术Ann. Comb. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Richaud–Degert Real Quadratic Fields and Maass Waveforms
Annals of Combinatorics ( IF 0.6 ) Pub Date : 2019-11-20 , DOI: 10.1007/s00026-019-00458-3
Larry Rolen , Karen Taylor

In this paper, we place the work of Andrews et al. (Invent Math 91(3):391–407, 1988) and Cohen (Invent Math 91(3):409–422, 1988), relating arithmetic in \({{\mathbb {Q}}}(\sqrt{6})\) to modularity of Ramanujan’s function \(\sigma (q)\), in the context of the general family of Richaud–Degert real quadratic fields \({{\mathbb {Q}}}(\sqrt{2p})\). Moreover, we give the resulting generalizations of the function \(\sigma \) as indefinite theta functions and invoke Zwegers’ work, (Q J Math 63(3):753–770, 2012), to prove the modular properties of the completed functions.

中文翻译:

Richaud–Degert实数二次场和马斯波形

在本文中,我们放置了Andrews等人的工作。(Invent Math 91(3):391–407,1988)和Cohen(Invent Math 91(3):409–422,1988),将\({{\ mathbb {Q}}}(\ sqrt {6 })\)到Ramanujan函数\(\ sigma(q)\)的模块化,在Richaud–Degert实数二次字段的一般族\\ {{{\ mathbb {Q}}}(\ sqrt {2p} )\)。此外,我们将函数\(\ sigma \)的结果推广为不定theta函数,并调用Zwegers的工作(QJ Math 63(3):753–770,2012),以证明已完成函数的模块性质。
更新日期:2019-11-20
down
wechat
bug