Zeros of order 2 of Dedekind zeta functions and Artin's Conjecture
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) ...
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For any Galois extension of number fields K/k, the object of this note is to show that if the quotient ζK(s)/ζk(s) of the Dedekind zeta functions has a zero of order at most max{2, p2 − 2} at s0 6= 1, then every Artin L-function for Gal(K/k) is holomorphic at s0, where p2 is the second smallest prime divisor of the degree of K/k. This result gives a refinement of the work of Foote and V. K. Murty.
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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...
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در این پایان نامه، در ابتدا برای مدول ها روی دامنه های پروفر شرایط معادل به دست آورده ایم و خواصی از ددکیند مدول ها روی دامنه های پروفر مشخص کرده ایم. در ادامه برای ددکیند مدول های با تولید متناهی روی حلقه های به طور صحیح بسته شرایط معادل به دست آورده ایم و ددکیند مدول های ضربی را مشخص کرده ایم. گزاره هایی در مورد بعد ددکیند مدول ها بیان کرده ایم. در پایان، قضایای lying over و going down را برا...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1990
ISSN: 0021-8693
DOI: 10.1016/0021-8693(90)90173-l