By Pei-Chu Hu
ISBN-10: 9048155460
ISBN-13: 9789048155460
ISBN-10: 9401594155
ISBN-13: 9789401594158
Nevanlinna thought (or worth distribution thought) in advanced research is so appealing that one may clearly have an interest in picking out how this sort of thought may glance within the non Archimedean research and Diophantine approximations. There are "main theorems" and disorder relatives that occupy a relevant position in N evanlinna thought. They generate loads of purposes in learning distinctiveness of meromorphic capabilities, international recommendations of differential equations, dynamics, and so forth. during this e-book, we are going to introduce non-Archimedean analogues of Nevanlinna thought and its functions. In worth distribution concept, the most challenge is that given a holomorphic curve f : C -+ M right into a projective sort M of size n and a kinfolk 01 of hypersurfaces on M, below a formal situation of non-degeneracy on f, locate the disorder relation. If 01 n is a relations of hyperplanes on M = r generally place and if the smallest measurement of linear subspaces containing the picture f(C) is ok, Cartan conjectured that the sure of illness relation is 2n - okay + 1. more often than not, if 01 is a kinfolk of admissible or common crossings hypersurfaces, there are respectively Shiffman's conjecture and Griffiths-Lang's conjecture. the following we record the method of this challenge: A. complicated research: (i) consistent goals: R. Nevanlinna[98] for n = ok = 1; H. Cartan [20] for n = ok > 1; E. I. Nochka [99], [100],[101] for n > ok ~ 1; Shiffman's conjecture partly solved by way of Hu-Yang [71J; Griffiths-Lang's conjecture (open).
Read Online or Download Meromorphic Functions over Non-Archimedean Fields PDF
Similar functional analysis books
This graduate-level textual content deals a survey of the most rules, options, and techniques that represent nonlinear useful research. It positive aspects broad statement, many examples, and fascinating, tough workouts. subject matters comprise measure mappings for limitless dimensional areas, the inverse functionality conception, the implicit functionality thought, Newton's tools, and lots of different matters.
A Basis Theory Primer: Expanded Edition
The classical topic of bases in Banach areas has taken on a brand new existence within the sleek improvement of utilized harmonic research. This textbook is a self-contained advent to the summary idea of bases and redundant body expansions and its use in either utilized and classical harmonic research. The 4 elements of the textual content take the reader from classical useful research and foundation thought to fashionable time-frequency and wavelet concept.
INVERSE STURM-LIOUVILLE PROBLEMS AND THEIR APPLICATIONS
This ebook offers the most effects and techniques on inverse spectral difficulties for Sturm-Liouville differential operators and their functions. Inverse difficulties of spectral research consist in improving operators from their spectral features. Such difficulties frequently seem in arithmetic, mechanics, physics, electronics, geophysics, meteorology and different branches of traditional sciences.
- Unbounded linear operators: theory and applications
- Function Theory on Manifolds Which Possess a Pole
- Advanced Real Analysis
Extra info for Meromorphic Functions over Non-Archimedean Fields
Example text
22. Let f be a non-constant meromorphic function in distinct numbers of K. Dejine 0= n:jn{l, 'Tl lai - ajl}, < 2N(r, J) , + t N (r, f -N2 ,Ram(r, J) - 2logr where Sf = L~ logfJ(po, f - and let a1, ... , a q be = max{l, laii}. A Then (q - l)T(r, J) K ~ aJ + Sf aj) -logfJ(po, f" ) + (q A -1) log I· j=1 Proof. Write f = h/ fo, where fo, h Fo = fo, Fi = h - a;Jo (i = 1,2, ... k(z)1 ::; Amax{lFo(z)l, lFi(Z)I} (k = 0, 1). , W 2i =W2, Next we fix z E K - i=1,2, ... ,q. K[O; Pol such that W 2 (z),h(z),Fi (z) =1O, i=O,l, ...
Then j - balsa admits k zeros in ,,[0; 1"] (counting multiplicity). Proof. Write j(z) = I:~=oanzn. 21, we have k = lI(r,f) and hence lanlr n S; lakl rk (n < k), lanlr n < laklrk (n> k). 30, one has lao - bl S; suplanlr n S; lakl rk , n2':l and hence lI(r, j - b) = k = lI(r, f). 21 again. 32. Assume that j E A(p(") (0< p S; 00) is unbounded. Then tor any b E ", we have N(1", j ~ b) = N(1", :7 ) + 0(1) (1" --t p). Proof. Note that j and j -b all have at least one zero since j -b also is unbounded.
Take I; E M(p(K) (i N (r,tl;) ~t N(r, = 1,2, ... ,k). Thenforr > 0, we have 1;), N (r,gl;) ~ tN(r,J;). 2. Take I; E M(p(K) (i m (r, g1;) ~ t = 1,2, ... , k). i), m (r, m(r, fi)· As usual, we define the characteristic function: T(r, J) = m(r, 1) + N(r, J) (Po< r < 00). Note that log J-L(r, J) = log + J-L ( r, ) f -log+ J-L(r,1 J) m(r, J) - m (r, ]-) . 2) can be rewritten as T (r,]- ) = T(r, J) -logJ-L(po, J). If f is a non-constant meromorphic function on J) N (r, -+ 00 or N(r, J) -+ have the following fact: 00.