Transcendental Values of a Class of Functions
نویسندگان
چکیده
منابع مشابه
Transcendental values of class group L - functions
Let K be an algebraic number field and f a complex-valued function on the ideal class group of K . Then, f extends in a natural way to the set of all non-zero ideals of the ring of integers of K and we can consider the Dirichlet series L(s, f ) = ∑a f (a)N(a)−s which converges for (s) > 1. After extending this function to (s) = 1, and in the case that f does not contain the trivial character, w...
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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 l...
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ژورنال
عنوان ژورنال: Indagationes Mathematicae (Proceedings)
سال: 1963
ISSN: 1385-7258
DOI: 10.1016/s1385-7258(63)50038-9