Real zeros of quadratic Dirichlet L-functions
نویسندگان
چکیده
منابع مشابه
Real zeros of quadratic Dirichlet L - functions
A small part of the Generalized Riemann Hypothesis asserts that L-functions do not have zeros on the line segment ( 2 , 1]. The question of vanishing at s = 2 often has deep arithmetical significance, and has been investigated extensively. A persuasive view is that L-functions vanish at 2 either for trivial reasons (the sign of the functional equation being negative), or for deep arithmetical r...
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Let χ be a primitive, real and even Dirichlet character with conductor q, and let s be a positive real number. An old result of H. Davenport is that the cycle sums Sν(s, χ) = ∑(ν+1)q−1 n=νq+1 χ(n) ns , ν = 0, 1, 2, . . . , are all positive at s = 1, and this has the immediate important consequence of the positivity of L(1, χ). We extend Davenport’s idea to show that in fact for ν ≥ 1, Sν(s, χ) ...
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ژورنال
عنوان ژورنال: Inventiones mathematicae
سال: 2002
ISSN: 0020-9910,1432-1297
DOI: 10.1007/s00222-002-0227-x