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 ...
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ROBERT C. RHOADES Abstra t. We show that the prime divisors of a random polynomial in Fq[t] are typi ally Poisson Distributed . This result is analogous to the result in Z of Granville [1℄. Along the way, we use a sieve developed by Granville and Soundararajan [2℄ to give a simple proof of the Erdös-Ka theorem in the fun tion eld setting. This approa h gives stronger results about the moments o...
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Let E/k(T ) be an elliptic curve defined over a rational function field of characteristic zero. Fix a Weierstrass equation for E. For points R ∈ E(k(T )), write xR = AR/D2 R with relatively prime polynomials AR(T ), DR(T ) ∈ k[T ]. The sequence {DnR}n≥1 is called the elliptic divisibility sequence of R. Let P, Q ∈ E(k(T )) be independent points. We conjecture that deg ( gcd(DnP , DmQ) ) is boun...
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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...
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ژورنال
عنوان ژورنال: Proceedings of the Japan Academy, Series A, Mathematical Sciences
سال: 1975
ISSN: 0386-2194
DOI: 10.3792/pja/1195518510