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DC Field | Value | Language |
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dc.contributor.advisor | D'Andrea, Carlos, 1973- | - |
dc.contributor.author | Quingles i Davı́, Guillem | - |
dc.date.accessioned | 2022-05-13T09:48:41Z | - |
dc.date.available | 2022-05-13T09:48:41Z | - |
dc.date.issued | 2021-06-20 | - |
dc.identifier.uri | http://hdl.handle.net/2445/185526 | - |
dc.description | Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2021, Director: Carlos D'Andrea | ca |
dc.description.abstract | [en] We follow the work of DeFranco in [4] and [5] to prove a factorization formula for the Taylor series coefficients of a zero of a polynomial as a function of the polynomial’s coefficients. This result extends to more general functions which we call complex exponent polynomials and also to the sum of a complex exponent polynomial and an holomorphic function with a simple zero. To prove this formula we need lemmas about Stirling numbers, multisets and partition sets. We also show that, when applied to polynomials, the formula recovers Sturmfels results in [11]. Finally, continuing the the work of DeFranco, we see that the formula, when applied to second degree polynomials, agrees with the known radical solutions and we prove an extension of a result about derivations on commutative rings. | ca |
dc.format.extent | 54 p. | - |
dc.format.mimetype | application/pdf | - |
dc.language.iso | cat | ca |
dc.rights | cc-by-nc-nd (c) Guillem Quingles i Davı́, 2021 | - |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/3.0/es/ | * |
dc.source | Treballs Finals de Grau (TFG) - Matemàtiques | - |
dc.subject.classification | Combinatòria (Matemàtica) | ca |
dc.subject.classification | Treballs de fi de grau | - |
dc.subject.classification | Funcions de diverses variables complexes | ca |
dc.subject.classification | Funcions holomorfes | ca |
dc.subject.other | Combinations | en |
dc.subject.other | Bachelor's theses | - |
dc.subject.other | Functions of several complex variables | en |
dc.subject.other | Holomorphic functions | en |
dc.title | Sèries de Taylor de zeros de polinomis d’exponents complexos | ca |
dc.type | info:eu-repo/semantics/bachelorThesis | ca |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | ca |
Appears in Collections: | Treballs Finals de Grau (TFG) - Matemàtiques |
Files in This Item:
File | Description | Size | Format | |
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tfg_quingles_davi_guillem.pdf | Memòria | 742.41 kB | Adobe PDF | View/Open |
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