Value Distribution Theory:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1993
|
| Subjects: | |
| Online Access: | Volltext |
| Item Description: | It is well known that solving certain theoretical or practical problems often depends on exploring the behavior of the roots of an equation such as (1) J(z) = a, where J(z) is an entire or meromorphic function and a is a complex value. It is especially important to investigate the number n(r, J = a) of the roots of (1) and their distribution in a disk Izl ~ r, each root being counted with its multiplicity. It was the research on such topics that raised the curtain on the theory of value distribution of entire or meromorphic functions. In the last century, the famous mathematician E. Picard obtained the pathbreaking result: Any non-constant entire function J(z) must take every finite complex value infinitely many times, with at most one exception. Later, E. Borel, by introducing the concept of the order of an entire function, gave the above result a more precise formulation as follows. An entire function J (z) of order A( 0 < A < (0) satisfies -1' logn(r, J = a) \ 1m = 1\ r->oo logr for every finite complex value a, with at most one exception. This result, generally known as the Picard-Borel theorem, lay the foundation for the theory of value distribution and since then has been the source of many research papers on this subject |
| Physical Description: | 1 Online-Ressource (XII, 269 p) |
| ISBN: | 9783662029152 9783662029176 |
| DOI: | 10.1007/978-3-662-02915-2 |
Staff View
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| 500 | |a It is well known that solving certain theoretical or practical problems often depends on exploring the behavior of the roots of an equation such as (1) J(z) = a, where J(z) is an entire or meromorphic function and a is a complex value. It is especially important to investigate the number n(r, J = a) of the roots of (1) and their distribution in a disk Izl ~ r, each root being counted with its multiplicity. It was the research on such topics that raised the curtain on the theory of value distribution of entire or meromorphic functions. In the last century, the famous mathematician E. Picard obtained the pathbreaking result: Any non-constant entire function J(z) must take every finite complex value infinitely many times, with at most one exception. Later, E. Borel, by introducing the concept of the order of an entire function, gave the above result a more precise formulation as follows. An entire function J (z) of order A( 0 < A < (0) satisfies -1' logn(r, J = a) \ 1m = 1\ r->oo logr for every finite complex value a, with at most one exception. This result, generally known as the Picard-Borel theorem, lay the foundation for the theory of value distribution and since then has been the source of many research papers on this subject | ||
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Record in the Search Index
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| indexdate | 2024-07-10T01:21:13Z |
| institution | BVB |
| isbn | 9783662029152 9783662029176 |
| language | English |
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| spelling | Lo, Yang Verfasser aut Value Distribution Theory by Yang Lo Berlin, Heidelberg Springer Berlin Heidelberg 1993 1 Online-Ressource (XII, 269 p) txt rdacontent c rdamedia cr rdacarrier It is well known that solving certain theoretical or practical problems often depends on exploring the behavior of the roots of an equation such as (1) J(z) = a, where J(z) is an entire or meromorphic function and a is a complex value. It is especially important to investigate the number n(r, J = a) of the roots of (1) and their distribution in a disk Izl ~ r, each root being counted with its multiplicity. It was the research on such topics that raised the curtain on the theory of value distribution of entire or meromorphic functions. In the last century, the famous mathematician E. Picard obtained the pathbreaking result: Any non-constant entire function J(z) must take every finite complex value infinitely many times, with at most one exception. Later, E. Borel, by introducing the concept of the order of an entire function, gave the above result a more precise formulation as follows. An entire function J (z) of order A( 0 < A < (0) satisfies -1' logn(r, J = a) \ 1m = 1\ r->oo logr for every finite complex value a, with at most one exception. This result, generally known as the Picard-Borel theorem, lay the foundation for the theory of value distribution and since then has been the source of many research papers on this subject Mathematics Global analysis (Mathematics) Analysis Mathematik Wertverteilungstheorie (DE-588)4137510-5 gnd rswk-swf Funktionentheorie (DE-588)4018935-1 gnd rswk-swf Wertverteilungstheorie (DE-588)4137510-5 s 1\p DE-604 Funktionentheorie (DE-588)4018935-1 s 2\p DE-604 https://doi.org/10.1007/978-3-662-02915-2 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Lo, Yang Value Distribution Theory Mathematics Global analysis (Mathematics) Analysis Mathematik Wertverteilungstheorie (DE-588)4137510-5 gnd Funktionentheorie (DE-588)4018935-1 gnd |
| subject_GND | (DE-588)4137510-5 (DE-588)4018935-1 |
| title | Value Distribution Theory |
| title_auth | Value Distribution Theory |
| title_exact_search | Value Distribution Theory |
| title_full | Value Distribution Theory by Yang Lo |
| title_fullStr | Value Distribution Theory by Yang Lo |
| title_full_unstemmed | Value Distribution Theory by Yang Lo |
| title_short | Value Distribution Theory |
| title_sort | value distribution theory |
| topic | Mathematics Global analysis (Mathematics) Analysis Mathematik Wertverteilungstheorie (DE-588)4137510-5 gnd Funktionentheorie (DE-588)4018935-1 gnd |
| topic_facet | Mathematics Global analysis (Mathematics) Analysis Mathematik Wertverteilungstheorie Funktionentheorie |
| url | https://doi.org/10.1007/978-3-662-02915-2 |
| work_keys_str_mv | AT loyang valuedistributiontheory |