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Topic: Nevanlinna theory

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	Rolf Nevanlinna - Wikipedia, the free encyclopedia
		Rolf Herman Nevanlinna (October 22, 1895, Joensuu - May 28, 1980, Helsinki) is perhaps the most famous Finnish mathematician.
		He was particularly appreciated for his work in theory of functions (i.e., complex analysis).
		His opinions in politics were sometimes somewhat controversial, but his talents as an amateur musician were widely appreciated.
	en.wikipedia.org /wiki/Rolf_Nevanlinna (118 words)

	Nevanlinna
		Nevanlinna was offered Weyl's chair when he left Zurich but refused.
		The main results of Nevanlinna theory appeared in a 100 page paper in 1925.
		Since 1982, an award, the Rolf Nevanlinna Prize, is presented at the International Congress of Mathematicians.
	www-groups.dcs.st-and.ac.uk /~history/Mathematicians/Nevanlinna.html (398 words)

	International Mathematical Union (IMU)
		The Rolf Nevanlinna Prize Committee is chosen by the Executive Committee of the International Mathematical Union.
		The Rolf Nevanlinna Prize in mathematical aspects of information science was established by the Executive Committee of the International Mathematical Union (IMU) in April 1981.
		The prize was named the Rolf Nevanlinna Prize in honor of Rolf Nevanlinna (1895-1980), who had been Rector of the University of Helsinki and President of the IMU and who in the 1950s had taken the initiative to the computer organization at Finnish universities.
	www.mathunion.org /General/Prizes/Nevanlinna (385 words)

	Dinghas (Site not responding. Last check: 2007-10-15)
		His most important work was in function theory, in particular Nevanlinna theory and the growth of subharmonic functions.
		Examples are the formula of Plana-Abel-Cauchy, the theorem of Julia-Wolff-Caratheodory, and the theory of Nevanlinna and of Hallstrom.
		The final part containing chapters on the maximum principle and the distribution of values, geometric function theory and conformal mapping, and Nevanlinna theory.
	www-history.mcs.st-and.ac.uk /history/Mathematicians/Dinghas.html (866 words)

	William A. Cherry's Publications
		Ye, Non-Archimedean Nevanlinna theory in several variables and the non-Archimedean Nevanlinna inverse problem, Trans.
		Cherry, "The Nevanlinna error term for coverings, generically surjective case," in W. Stoll, ed., Proceedings of the Symposium on Value Distribution Theory in Several Complex Variables, Notre Dame Mathematical Lectures 12, University of Notre Dame Press, 1992.
		Cherry, Topics in p-adic function theory, text of a lecture delivered at the symposium on p-adic Nevanlinna theory and related topics, held at the Nippon Institute of Technology, November 1998.
	wcherry.math.unt.edu /pubs.html (364 words)

	Acquisitions in Mathematics 2002, page 5 (515-515.99) - Mathematics - LEARN - The University of Auckland Library
		Nevanlinna's theory of value distribution: the second main theorem and its error terms / William Cherry, Zhuan Ye.
		Nevanlinna theory and its relation to Diophantine approximation / Min Ru.
		Regularity theory of Fourier integral operators with complex phases and singularities of affine fibrations / M. Ruzhansky.
	www.library.auckland.ac.nz /subjects/math/older/2002p5.htm (3149 words)

	AMCA: Foundations of the Spectral Theory of Nevanlinna's Mapping from a Topological Space to the Algebra of ...
		AMCA: Foundations of the Spectral Theory of Nevanlinna's Mapping from a Topological Space to the Algebra of Endomorphisms of a Banach Space and its Applications by M. Ragimov
		The spectral theory and functional calculus for an infinite number of closed commutaing operators was constructed.
		This theory opens new directions in the multidimensional spectral analysis of linear operators and its applications in theoretical physics, and to theory of multidimensional differential equations in Banach space.
	at.yorku.ca /c/a/g/x/63.htm (363 words)

	On Nevanlinna's Secondary Deficiency (ResearchIndex)
		Analogies between the Nevanlinna theory and the theory of heights in number theory have motivated to the determination the precise error term of the second fundamental theorem of the Nevanlinna theory.
		The Nevanlinna secondary deficiency, introduced by P.M. Wong, gives the error term in a certain sense.
		We first prove that, from a topological point of view, almost all meromorphic functions have secondary deficiency negative infinity and that the set of meromorphic functions having maximum...
	citeseer.ist.psu.edu /339969.html (314 words)

	Amazon.ca: Books: Nevanlinna Theory and Its Relation to Diophantine Approximation (Site not responding. Last check: 2007-10-15)
		Nevanlinna Theory and Its Relation to Diophantine Approximation
		This book provides an introduction to both Nevanlinna theory and Diophantine approximation, with emphasis on the analogy between these two subjects.
		Each chapter is divided into part A and part B. Part A deals with Nevanlinna theory and part B covers Diophantine approximation.
	www.amazon.ca /exec/obidos/ASIN/9810244029 (323 words)

	Mathematics Colloquium: Tohge Abstract, Spring 2005
		The purpose of this talk is to give a survey of the value distribution theory of meromorphic functions on (C) and holomorphic curves into the projective space P(C) from the viewpoint of the functional equation
		R. Nevanlinna's value distribution theory is an effective method of investigating the non-existence of non-trivial meromorphic solutions of the Fermat equation f
		Many of the topics overlap with those in the paper, G.G. Gundersen and W.K. Hayman, The Strength of Cartan's version of Nevanlinna Theory, Bull.
	www.math.uiuc.edu /Colloquia/05SP/tohge_mar17-05.html (212 words)

	Web Comics: : Science : Math : Number Theory : People : V web sites (Site not responding. Last check: 2007-10-15)
		Algebraic number theory, analytic number theory, class field theory and theory of algebraic functions.
		Iwasawa theory of p-adic Lie extensions; arithmetic of elliptic curves, Selmer groups of abelian varieties, structure of profinite (or pro-p) groups.
		Diophantine approximation; Nevanlinna theory, especially as related to diophantine approximation; Arakelov theory.
	www.webcomics.com /top/index.php/Science/Math/Number_Theory/People/V (601 words)

	Publications of Paul Vojta
		This preprint gives an expository introduction to the theory of jet spaces on arbitrary schemes, defined using Hasse-Schmidt derivations.
		In: W. Stoll, ed., Proceedings Symposium on Value Theory in Several Complex Variables, Notre Dame, Indiana, April, 1990, University of Notre Dame Press, Notre Dame, 1992, pp.
		In: Advances in Number Theory (Proceedings of the Canadian Number Theory Association, Queens University, Kingston, Ontario, August, 1991), Fernando Q. Gouvea and Noriko Yui, eds., Clarendon Press, Oxford, 1993, pp.
	math.berkeley.edu /~vojta/bib.html (522 words)

	Applications Of Explicit Error Terms In Nevanlinna Theory (ResearchIndex)
		1 A sharp form of Nevanlinna's second main theorem of several..
		1 the second main theorem of Nevanlinna theory (context) - to, Wong et al.
		1 Second main theorem of Nevanlinna theory for non-equidimensi..
	citeseer.ist.psu.edu /209577.html (478 words)

	American Mathematical Monthly, The: Nevanlinna's Theory of Value Distribution: The Second Main Theorem and its Error ... (Site not responding. Last check: 2007-10-15)
		Nevanlinna's Theory of Value Distribution: The Second Main Theorem and its Error Terms
		Complex Analysis, P. Nevanlinna's Theory of Value Distribution: The Second Main Theorem and its Error Terms.
		Nevanlinna theory gives information on how often it takes a given value within a circle of prescribed radius.
	www.findarticles.com /p/articles/mi_qa3742/is_200211/ai_n9122168 (189 words)

	11J: Diophantine approximation, transcendental number theory
		11J89: Transcendence theory of elliptic and abelian functions
		11J93: Transcendence theory of Drinfel´d and t-modules [new in 2000]
		11J97: Analogues of methods in Nevanlinna theory (work of Vojta et al.) [new in 2000]
	www.math.niu.edu /~rusin/known-math/index/11JXX.html (343 words)

	NEVANLINNA THEORY AND ITS RELATION TO DIOPHANTINE APPROXIMATION
		It was discovered recently that Nevanlinna theory and Diophantine approximation bear striking similarities and connections.
		Nevanlinna Theory for Meromorphic Functions and Roth's Theorem
		Readership: Researchers in complex analysis, number theory and complex geometry.
	www.worldscibooks.com /mathematics/4508.html (160 words)

	pub97
		Geometric topology, low-dimensional topology, knot theory, foliations and laminations in 3-manifolds
		A theorem in the representation theory of totally disconnected groups, Proceedings of the American Mathematical Society, volume 45, number 3, 1974, pp.
		A characterization of orthogonal duality in matroid theory, Geometriae Dedicata 15(l983), 69-72.
	www.math.unt.edu /~bator (8099 words)

	Research (Site not responding. Last check: 2007-10-15)
		Minimal surfaces, Mean curvature flow, Harmonic functions and Laplace Eigenfunctions on Riemannian manifolds, Nonlinear waves, Microlocal analysis of spectral and scattering problems, Bochner-Riesz means, Nevanlinna theory.
		Mori program: birational classification of varieties, minimal models; Hodge theory, geometry of Shimura varieties, vanishing theorems, moduli of vector bundles, meromorphic mappings, Nevanlinna theory, complex dynamics, Teichmueller theory.
		Classical field theories, quantum cohomology, quantum chaos, quantum gravity, Branes and calibrated geometries esp special Lagrangian geometry, Discrete breathers.
	mathnt.mat.jhu.edu /mathnew/research.html (128 words)

	Homepage of Grigor Barsegian (Site not responding. Last check: 2007-10-15)
		Supervisor of Research Project ''Geometrical theory of complex functions'' at Institute of Mathematics National Acad.
		Barsegian G., In the path from past to future of the theory of meromorphic functions, Short communications, Intern.
		Barsegian G. and Begehr H., Lines of catastrophe: problems, examples of solutions, connections with Nevanlinna theory and Gamma-lines, Third ISAAC Congress, Freie Universitat Berlin, August 20-25, 2001, Plenary and selected lectures, World Scientific, 2003.
	math.sci.am /People/GrigorBarsegian.html (1241 words)

	JAMI Seminars (JHU-Math) (Site not responding. Last check: 2007-10-15)
		Bernard Shiffman of the Johns Hopkins University will speak on Introduction to Nevanlinna Theory, I. This is the first of a series of talks.
		We will begin with a self-contained introduction to value distribution theory in one complex variable.
		Graduate students are encouraged to attend and may enroll in 110.762.
	www.math.jhu.edu /seminars/jamisem.html (299 words)

	Transactions of the American Mathematical Society
		Hasse, H. and Schmidt, F. Noch eine Bergründung der Theorie der höheren Differentialquotienten in einem algebraischen Funktionenkörper einer Unbestimmtten, J. Reine Angew.
		Okugawa, K., Basic properties of differential fields of an arbitrary characteristic and the Picard-Vessiot theory, J. Math.
		Stoll, W. and Wong, P.-M., Second main theorem of Nevanlinna theory for nonequidimensional meromorphic maps, Amer.
	www.ams.org /tran/2004-356-07/S0002-9947-03-03363-4/home.html (380 words)

	XVIII Nevanlinna Colloquium - Abstracts
		Manju Rani Agrawal: Korovkin theory in commutative Banach algebras
		Katsuya Ishizaki: Nevanlinna theory and some functional equations
		Corneliu Udrea: Non-linear potential theory: the boundedness and the complete maximum principle
	www.math.helsinki.fi /~analysis/NevanlinnaColloquium/abstracts (677 words)

	[No title] (Site not responding. Last check: 2007-10-15)
		Subject: Re: books on Nevanlinna theory Date: 01 Mar 1999 13:27:55 -0600 Newsgroups: sci.math.research Xiao-Song Lin
		Another classic is: W. Hayman, Meromorphic Functions, Clarendon Press, Oxford, 1964 (out of print) If you read Russian, a very nice book is: Goldberg and Ostrovskii, Distribution of Values of Meromorphic Functions, Nauka 1970 If you read German, you may like: G. Jank and L. Volkmann, Meromorphe Funktionen und Differentialgleichungen, Birkhauser Verlag, 1985.
		If you're particularly interested in applications to differential equations, there is: I. Laine, Nevanlinna Theory and Differential Equations, de Gruyter Studies in Math.
	www.math.niu.edu /~rusin/known-math/99/nevanlinna (122 words)

	A Nevanlinna--Pick Approach to Time-Domain Constrained i Control (Site not responding. Last check: 2007-10-15)
		A Nevanlinna--Pick Approach to Time-Domain Constrained i Control: SIAM Journal on Control and Optimization Vol.
		In this paper, generalized Nevanlinna--Pick theory is used to solve a time-domain constrained $i$ control problem for linear time-invariant discrete-time systems.
		First it is shown that if constraints are imposed only over a finite horizon (i.e., only on the first $n$ samples), then the problem reduces to a finite-dimensional convex minimization problem.
	epubs.siam.org /sam-bin/dbq/article/24988 (127 words)

	Best Book Buys - Value distribution theory Books (Site not responding. Last check: 2007-10-15)
		by Alexander Dinghas, Rolf Herman Nevanlinna, Cabiria Andreian Cazacu
		Value Distribution Theory and Complex Dynamics: Proceedings of the Special Session on Value Distribution Theory and Complex Dynamics of the First Joint International Meeting of the American
		Proceedings Symposium on Value Distribution Theory in Several Complex Variables: Symposium on Value Distribution Theory in Several Complex Variables On the Occasion of the Inauguration of Wilhelm Stoll As the Vincent F. Duncan
	www.bestwebbuys.com /Mathematics-General-N_10020883-books.html (226 words)

	Open Directory - Science: Math: Number Theory: People: V (Site not responding. Last check: 2007-10-15)
		Waring's problem, the Goldbach problem, the Hardy-Littlewood method, the use of "smooth" numbers, the distribution of primes, exponential sums over integer sequences, properties of the Riemann zeta-function and Dirichlet L-functions.
		Venkov, Boris - Laboratory of Algebra and Number Theory, Petersburg Department of Steklov Institute of Mathematics.
		Vsemirnov, Maxim - Sidney Sussex College, Cambridge (on leave from Steklov Institute of Mathematics, St. Petersburg).
	dmoz.org /Science/Math/Number_Theory/People/V (319 words)

	A more general abc conjecture, by Paul Vojta (Site not responding. Last check: 2007-10-15)
		It also shows that the new conjecture is implied by the earlier conjecture.
		As with most of the author's conjectures, this new conjecture stems from analogies with Nevanlinna theory; in this case it corresponds to a Second Main Theorem in Nevanlinna theory with truncated counting functions.
		The original abc conjecture of Masser and Oesterlé corresponds to the Second Main Theorem with truncated counting functions on
	www.math.uiuc.edu /Algebraic-Number-Theory/0118 (104 words)

	MSC 2000 : CC = Van
		11J97 Analogues of methods in Nevanlinna theory (work of Vojta et al.) [
		20F06 Cancellation theory; application of van Kampen diagrams [See also 57M05]
		32A22 Nevanlinna theory (local); growth estimates; other inequalities [For geometric theory, see 32H25, 32H30]
	math-doc.ujf-grenoble.fr /cgi-bin/msc2000.py?L=en&T=Q&C=msc2000&CC=Van (139 words)

	Amazon.ca: Books: Meromorphic Functions Over Non-Archimedean Fields (Site not responding. Last check: 2007-10-15)
		An introduction to value distribution theory over non-Archimedian fields.
		Gives applications for the theory and suggests new problems for further research.
		Look for books like Meromorphic Functions Over Non-Archimedean Fields by subject:
	www.amazon.ca /exec/obidos/ASIN/0792365321 (127 words)

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