Zeta functions of regular arithmetic schemes at s=0
نویسندگان
چکیده
منابع مشابه
Artin-mazur Zeta Functions in Arithmetic Dynamics
This is a special case of an Artin-Mazur zeta function, which is defined for certain dynamical systems (and in general counts the number of isolated fixed points). Note that we are, as usual, not counting fixed points with multiplicity, which in this case would be something like the Lefschetz index. In fact, if we did count with multiplicity and deg f = d, then |Pern(f)| = d + 1 for all n, and ...
متن کاملSchemes over F1 and Zeta Functions
We develop a theory of schemes over the field of characteristic one which reconciles the previous attempts by Soulé and by Deitmar. Our construction fits with the geometry of monoids of Kato and is no longer limited to toric varieties. We compute the zeta function of an arbitrary Noetherian scheme (over the field of characteristic one) and prove that the torsion in the local geometric structure...
متن کاملSchemes over F1 and Zeta Functions
We determine the real counting function N(q) (q ∈ [1,∞)) for the hypothetical “curve” C = Spec Z over F1, whose corresponding zeta function is the complete Riemann zeta function. We show that such counting function exists as a distribution, is positive on (1,∞) and takes the value −∞ at q = 1 as expected from the infinite genus of C. Then, we develop a theory of functorial F1-schemes which reco...
متن کاملArithmetic expressions of Selberg’s zeta functions for congruence subgroups
Abstract In [Sa], it was proved that the Selberg zeta function for SL2(Z) is expressed in terms of the fundamental units and the class numbers of the primitive indefinite binary quadratic forms. The aim of this paper is to obtain similar arithmetic expressions of the logarithmic derivatives of the Selberg zeta functions for congruence subgroups of SL2(Z). As applications, we study the Brun-Titc...
متن کاملLocal zeta functions and the arithmetic of moduli spaces
Hiroki Aoki On the structure theorem for modular forms ... Igusa’s result and beyond In this talk we treat the structure theorem of the graded ring of modular forms of several variables. Determining the structure is not easy in general. The first result was given by Professor Jun-Ichi Igusa in 1962. This was on the graded ring of Siegel modular forms of degree 2 of even weights. And then in 196...
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: Duke Mathematical Journal
سال: 2014
ISSN: 0012-7094
DOI: 10.1215/00127094-2681387