On Equivariant Dedekind Zeta - Functions at s = 1 Dedicated to Professor Andrei Suslin
نویسندگان
چکیده
We study a refinement of an explicit conjecture of Tate concerning the values at s = 1 of Artin L-functions. We reinterpret this refinement in terms of Tamagawa number conjectures and then use this connection to obtain some important (and unconditional) evidence for our conjecture. 2010 Mathematics Subject Classification: 11R42, 11R33
منابع مشابه
Zeros 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 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 کاملUpper bounds for residues of Dedekind zeta functions and class numbers of cubic and quartic number fields
Let K be an algebraic number field. Assume that ζK(s)/ζ(s) is entire. We give an explicit upper bound for the residue at s = 1 of the Dedekind zeta function ζK(s) of K. We deduce explicit upper bounds on class numbers of cubic and quartic number fields.
متن کاملOn the Euler Product of Some Zeta Functions
It is well-known that the Euler product for the Riemann zeta function ζ(s) is still valid for !(s) = 1 and s "= 1. In this paper, we extend this result to zeta functions of number fields. In particular, the Dedekind zeta function ζk(s) for any algebraic number field k and the Hecke zeta function ζ(s,χ) for the rational number field are shown to have the Euler product on the line !(s) = 1 except...
متن کاملEXPLICIT UPPER BOUNDS FOR THE RESIDUES AT s = 1 OF THE DEDEKIND ZETA FUNCTIONS OF SOME TOTALLY REAL NUMBER FIELDS
— We give an explicit upper bound for the residue at s = 1 of the Dedekind zeta function of a totally real number field K for which ζK(s)/ζ(s) is entire. Notice that this is conjecturally always the case, and that it holds true if K/Q is normal or if K is cubic. Résumé (Bornes supérieures explicites pour les résidus en s = 1 des fonctions zêta de Dedekind de corps de nombres totalement réels) N...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2010