Academic Journal
On the definition of higher Gamma functions
| العنوان: | On the definition of higher Gamma functions |
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| المؤلفون: | Pérez-Marco, Ricardo |
| المساهمون: | Institut de Mathématiques de Jussieu - Paris Rive Gauche (IMJ-PRG (UMR_7586)), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), Centre National de la Recherche Scientifique (CNRS) |
| المصدر: | ISSN: 0176-4276. |
| بيانات النشر: | HAL CCSD Springer Verlag |
| سنة النشر: | 2023 |
| مصطلحات موضوعية: | 2010 Mathematics Subject Classification. Primary: 33B15. Secondary: 30D10, 30D15 Gamma function, Barnes Gamma function, Mellin Gamma functions, Jackson q-Gamma function, multiple gamma functions, [MATH.MATH-CV]Mathematics [math]/Complex Variables [math.CV], [MATH.MATH-NT]Mathematics [math]/Number Theory [math.NT] |
| الوصف: | International audience ; We generalize our previous new definition of Euler Gamma function to higher Gamma functions. With this unified approach, we characterize Barnes higher Gamma functions, Mellin Gamma functions, Barnes multiple Gamma functions, Jackson q-Gamma function, and Nishizawa higher q-Gamma functions. This approach extends to more general functional equations. This generalization reveals the multiplicative group structure of solutions of the functional equation that appears as a cocycle equation. We also generalize Barnes hierarchy of higher Gamma function and multiple Gamma functions. In this new approach, Barnes-Hurwitz zeta functions are no longer required for the definition of Barnes multiple Gamma functions. This simplifies the classical definition, without the necessary analytic preliminaries about the meromorphic extension of Barnes-Hurwitz zeta functions, and defines a larger class of Gamma functions. For some algebraic independence conditions on the parameters, we have uniqueness of the solutions, which implies the coincidence of our multiple Gamma functions with Barnes multiple Gamma functions. |
| نوع الوثيقة: | article in journal/newspaper |
| اللغة: | English |
| Relation: | hal-03096445; https://hal.science/hal-03096445; https://hal.science/hal-03096445/document; https://hal.science/hal-03096445/file/definition-higher-gamma4.pdf |
| DOI: | 10.1007/s00365-023-09674-w |
| الاتاحة: | https://hal.science/hal-03096445 https://hal.science/hal-03096445/document https://hal.science/hal-03096445/file/definition-higher-gamma4.pdf https://doi.org/10.1007/s00365-023-09674-w |
| Rights: | info:eu-repo/semantics/OpenAccess |
| رقم الانضمام: | edsbas.B5F63FD8 |
| قاعدة البيانات: | BASE |
| DOI: | 10.1007/s00365-023-09674-w |
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