Periods of Modular Forms and Imaginary Quadratic Base Change

Canadian mathematical bulletin

Mak Trifković¹ 

[1] Mathematics and Statistics, University of Victoria, Victoria, BC, Canada

关键词: Nearly Kähler manifold;    6-dimension;    Homogeneous;    The 1st Chern Class;    Einstein manifolds;   

DOI  :  10.4153/CMB-2010-047-0

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

Let $f$ be a classical newform of weight $2$ on the upper half-plane $mathcal H^{(2)}$, $E$ the corresponding strong Weil curve, $K$ a class number one imaginary quadratic field, and $F$ the base change of $f$ to $K$. Under a mild hypothesis on the pair $(f,K)$, we prove that the period ratio $Omega_E/(sqrt{|D|}Omega_F)$ is in $mathbb Q$. Here $Omega_F$ is the unique minimal positive period of $F$, and $Omega_E$ the area of $E(mathbb C)$. The claim is a specialization to base change forms of a conjecture proposed and numerically verified by Cremona and Whitley.

【 授权许可】

Unknown