Abstract
Let K be an imaginary quadratic field and f an integral ideal. Denote by Cl(f) the ray class group of f. For every non-trivial character χ of Cl(f), we show that L(1, χ)/π is transcendental. If f = f, then complex conjugation acts on the character group of Cl(f). Denoting by Ĉl(f) + the orbits of the group of characters, we show that the values L(1, χ) as χ ranges over elements of Ĉl(f) + are linearly independent over Q. We give applications of this result to the study of transcendental values of Petersson inner products and certain special values of Artin L-series attached to dihedral extensions.
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