Purely Arithmetic PDEs Over a 𝑝-Adic Field: -Characters and -Modular Forms
A formalism of arithmetic partial differential equations (PDEs) is being developed in which one considers several arithmetic differentiations at one fixed prime. In this theory solutions can be defined in algebraically closed -adic fields. As an application we show that for at least two arithmetic d...
Kaydedildi:
| Asıl Yazarlar: | , |
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| Materyal Türü: | Livre numérique |
| Dil: | Anglais |
| Baskı/Yayın Bilgisi: |
Berlin :
European Mathematical Society
2023.
Berlin : |
| Seri Bilgileri: | Memoirs of the European Mathematical Society
6 |
| Online Erişim: | Accès sur la plateforme EMS Press Accès sur la plateforme ISTEX Accès Université d'Orléans Accès INSA CVL |
| Not: |
European Mathematical Society (Licence nationale) European Mathematical Society (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Purely Arithmetic PDEs Over a 𝑝-Adic Field: -Characters and -Modular Forms, 978-3-98547-057-0 |
| Özet: | A formalism of arithmetic partial differential equations (PDEs) is being developed in which one considers several arithmetic differentiations at one fixed prime. In this theory solutions can be defined in algebraically closed -adic fields. As an application we show that for at least two arithmetic directions every elliptic curve possesses a non-zero arithmetic PDE Manin map of order 1; such maps do not exist in the arithmetic ODE case. Similarly, we construct and study "genuinely PDE" differential modular forms. As further applications we derive a Theorem of the kernel and a Reciprocity theorem for arithmetic PDE Manin maps and also a finiteness Diophantine result for modular parameterizations. We also prove structure results for the spaces of "PDE differential modular forms defined on the ordinary locus". We also produce a system of differential equations satisfied by our PDE modular forms based on Serre and Euler operators. |
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| Diğer Bilgileri: | European Mathematical Society (Licence nationale) European Mathematical Society (Licence nationale) |
| ISBN: | 9783985475575 |
| ISSN: | 2747-9099 |
| Erişim: | Accès en ligne pour les établissements français bénéficiaires des licences nationales Accès soumis à abonnement pour tout autre établissement Conditions particulières de réutilisation pour les bénéficiaires des licences |