Geodesic
Periods of Modular Forms and Imaginary Quadratic Base Change
Canadian mathematical bulletin, Tome 53 (2010) no. 3, pp. 571-576

Voir la notice de l'article provenant de la source Cambridge University Press

Let $f$ be a classical newform of weight 2 on the upper half-plane ${{H}^{(2)}}$ , $E$ 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 ${{\Omega }_{E}}/(\sqrt{\left| D \right|}{{\Omega }_{F}})$ 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.
DOI : 10.4153/CMB-2010-047-0
Mots-clés : 11F67 
Trifković, Mak. Periods of Modular Forms and Imaginary Quadratic Base Change. Canadian mathematical bulletin, Tome 53 (2010) no. 3, pp. 571-576. doi: 10.4153/CMB-2010-047-0
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