Real zeros of Dedekind zeta functions of real quadratic fields
نویسندگان
چکیده
منابع مشابه
Real zeros of Dedekind zeta functions of real quadratic fields
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) ...
متن کاملReal 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...
متن کاملZeros of Dedekind zeta functions in the critical strip
In this paper, we describe a computation which established the GRH to height 92 (resp. 40) for cubic number fields (resp. quartic number fields) with small discriminant. We use a method due to E. Friedman for computing values of Dedekind zeta functions, we take care of accumulated roundoff error to obtain results which are mathematically rigorous, and we generalize Turing’s criterion to prove t...
متن کاملThe zeros of Dedekind zeta functions and class numbers of CM-fields
Let F ′/F be a finite normal extension of number fields with Galois group Gal(F ′/F ). Let χ be an irreducible character of Gal(F ′/F ) of degree greater than one and L(s, χ) the associated Artin L-function. Assuming the truth of Artin’s conjecture, we have explicitly determined a zero-free region about 1 for L(s, χ). As an application we show that, for a CM-field K of degree 2n with solvable n...
متن کاملDistribution of values of real quadratic zeta functions
The author has previously extended the theory of regular and irregular primes to the setting of arbitrary totally real number fields. It has been conjectured that the Bernoulli numbers, or alternatively the values of the Riemann zeta function at odd negative integers, are evenly distributed modulo p for every p. This is the basis of a well-known heuristic, given by Siegel in [16], for estimatin...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 2004
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-04-01701-6