Periods of Modular Forms and Imaginary Quadratic Base Change

• Autores: Mak Trifkovic
• Localización: Canadian mathematical bulletin, ISSN 0008-4395, Vol. 53, Nº 3, 2010, págs. 571-576
• Idioma: inglés
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• Resumen

  • 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 ?E/(v{|D|}?F) is in Q. Here ?F is the unique minimal positive period of F, and ?E the area of E(C). The claim is a specialization to base change forms of a conjecture proposed and numerically verified by Cremona and Whitley.