Periods of Modular Forms and Imaginary Quadratic Base Change
Canadian mathematical bulletin, Tome 53 (2010) no. 3, pp. 571-576
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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.
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
@article{10_4153_CMB_2010_047_0,
author = {Trifkovi\'c, Mak},
title = {Periods of {Modular} {Forms} and {Imaginary} {Quadratic} {Base} {Change}},
journal = {Canadian mathematical bulletin},
pages = {571--576},
year = {2010},
volume = {53},
number = {3},
doi = {10.4153/CMB-2010-047-0},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2010-047-0/}
}
TY - JOUR AU - Trifković, Mak TI - Periods of Modular Forms and Imaginary Quadratic Base Change JO - Canadian mathematical bulletin PY - 2010 SP - 571 EP - 576 VL - 53 IS - 3 UR - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2010-047-0/ DO - 10.4153/CMB-2010-047-0 ID - 10_4153_CMB_2010_047_0 ER -
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