Global ideal theory of meromorphic function fields
نویسندگان
چکیده
منابع مشابه
Global Ideal Theory of Meromorphic Function Fields
It is shown that the ideal theories of the fields of all meromorphic functions on any two noncompact Riemann surfaces are isomorphic. Further, various new representation and factorization theorems are proved. Introduction. Throughout this paper let X and Y denote noncompact (connected) Riemann surfaces. Let A(X) (or A for short), denote the ring of all analytic functions on X, and let F(X) (or ...
متن کاملIwasawa Theory of Zp-Extensions over Global Function Fields
In this paper we study the Iwasawa theory of Zp-extensions of global function fields k over finite fields of characteristic p. When d = 1 we first show that Iwasawa invariants are well defined under the assumption that only finitely many primes are ramified in the extension, then we prove that the Iwasawa μ-invariant can be arbitrarily large for some extension of any given base field k. After g...
متن کاملOn $L^*$-proximate order of meromorphic function
In this paper we introduce the notion of $L^{* }$-proximate order of meromorphic function and prove its existence.
متن کاملExplicit Class Field Theory for Global Function Fields
Let F be a global function field and let F ab be its maximal abelian extension. Following an approach of D. Hayes, we shall construct a continuous homomorphism ρ : Gal(F /F ) → CF , where CF is the idele class group of F . Using class field theory, we shall show that our ρ is an isomorphism of topological groups whose inverse is the Artin map of F . As a consequence of the construction of ρ, we...
متن کاملCharacteristic function of a meromorphic function and its derivatives
In this paper, some results of Singh, Gopalakrishna and Kulkarni (1970s) have been extended to higher order derivatives. It has been shown that, if $sumlimits_{a}Theta(a, f)=2$ holds for a meromorphic function $f(z)$ of finite order, then for any positive integer $k,$ $T(r, f)sim T(r, f^{(k)}), rrightarrowinfty$ if $Theta(infty, f)=1$ and $T(r, f)sim (k+1)T(r, f^{(k)}), rrightarrowinfty$ if $Th...
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: Transactions of the American Mathematical Society
سال: 1979
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1979-0546917-2