Localization of the first zero of the Dedekind zeta function
نویسنده
چکیده
Using Weil’s explicit formula, we propose a method to compute low zeros of the Dedekind zeta function. As an application of this method, we compute the first zero of the Dedekind zeta function associated to totally complex fields of degree less than or equal to 30 having the smallest known discriminant.
منابع مشابه
A NEW PROOF OF THE PERSISTENCE PROPERTY FOR IDEALS IN DEDEKIND RINGS AND PR¨UFER DOMAINS
In this paper, by using elementary tools of commutative algebra,we prove the persistence property for two especial classes of rings. In fact, thispaper has two main sections. In the first main section, we let R be a Dedekindring and I be a proper ideal of R. We prove that if I1, . . . , In are non-zeroproper ideals of R, then Ass1(Ik11 . . . Iknn ) = Ass1(Ik11 ) [ · · · [ Ass1(Iknn )for all k1,...
متن کاملZeros of Dedekind Zeta Functions and Holomorphy of Artin L-functions
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.
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 کاملAn improved upper bound for the error in the zero-counting formulae for Dirichlet L-functions and Dedekind zeta-functions
This paper contains new explicit upper bounds for the number of zeroes of Dirichlet L-functions and Dedekind zeta-functions in rectangles.
متن کاملEVALUATION OF THE DEDEKIND ZETA FUNCTIONS AT s = −1 OF THE SIMPLEST QUARTIC FIELDS
The simplest quartic field was introduced by M. Gras and studied by A. J. Lazarus. In this paper, we will evaluate the values of the Dedekind zeta functions at s = −1 of the simplest quartic fields. We first introduce Siegel’s formula for the values of the Dedekind zeta function of a totally real number field at negative odd integers, and will apply Siegel’s formula to the simplest quartic fiel...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Math. Comput.
دوره 70 شماره
صفحات -
تاریخ انتشار 2001