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P-adic analytic functions / Alain Escassut.

By: Escassut, Alain [author.].
Material type: TextTextPublisher: New Jersey : World Scientific, [2021]Description: viii, 340 pages; USD 128.00 25 cms.Content type: text Media type: unmediated Carrier type: volumeISBN: 9789811226212.Subject(s): p-adic analysis | Analytic functions | Nevanlinna theoryDDC classification: 512.7/4
Contents:
Ultrametric fields -- Analytic elements and analytic functions -- Meromorphic functions and Nevanlinna theory.
Summary: "P-adic Analytic Functions describes the definition and properties of p-adic analytic and meromorphic functions in a complete algebraically closed ultrametric field. Various properties of p-adic exponential-polynomials are examined, such as the Hermite Lindemann theorem in a p-adic field, with a new proof. The order and type of growth for analytic functions are studied, in the whole field and inside an open disk. P-adic meromorphic functions are studied, not only on the whole field but also in an open disk and on the complemental of a closed disk, using Motzkin meromorphic products. Finally, the p-adic Nevanlinna theory is widely explained, with various applications. Small functions are introduced with results of uniqueness for meromorphic functions. The question of whether the ring of analytic functions - in the whole field or inside an open disk - is a Bezout ring is also examined"-- Provided by publisher.
List(s) this item appears in: 2023-09-29
Item type Current location Call number Status Date due Barcode Item holds
Book Chennai Mathematical Institute
General Stacks 		512.74 ESC (Browse shelf) Available 11106
Total holds: 0

Includes bibliographical references and index.

Ultrametric fields -- Analytic elements and analytic functions -- Meromorphic functions and Nevanlinna theory.

"P-adic Analytic Functions describes the definition and properties of p-adic analytic and meromorphic functions in a complete algebraically closed ultrametric field. Various properties of p-adic exponential-polynomials are examined, such as the Hermite Lindemann theorem in a p-adic field, with a new proof. The order and type of growth for analytic functions are studied, in the whole field and inside an open disk. P-adic meromorphic functions are studied, not only on the whole field but also in an open disk and on the complemental of a closed disk, using Motzkin meromorphic products. Finally, the p-adic Nevanlinna theory is widely explained, with various applications. Small functions are introduced with results of uniqueness for meromorphic functions. The question of whether the ring of analytic functions - in the whole field or inside an open disk - is a Bezout ring is also examined"-- Provided by publisher.