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Search: MSC category 11F67
( Special values of automorphic $L$series, periods of modular forms, cohomology, modular symbols )
1. CMB 2010 (vol 53 pp. 571)
 Trifković, Mak

Periods of Modular Forms and Imaginary Quadratic Base Change
Let $f$ be a classical newform of weight $2$ on the upper halfplane $\mathcal H^{(2)}$, $E$ 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.
Category:11F67 

2. CMB 2005 (vol 48 pp. 535)