Multiplicity estimate for solutions of extended Ramanujan’s system

Evgeniy Zorin[1]

  • [1] Department of Mathematics University of York York, YO10 5DD, UK

Journal de Théorie des Nombres de Bordeaux (2012)

  • Volume: 24, Issue: 3, page 773-781
  • ISSN: 1246-7405

Abstract

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We establish a new multiplicity lemma for solutions of a differential system extending Ramanujan’s classical differential relations. This result can be useful in the study of arithmetic properties of values of Riemann zeta function at odd positive integers (Nesterenko, 2011).

How to cite

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Zorin, Evgeniy. "Multiplicity estimate for solutions of extended Ramanujan’s system." Journal de Théorie des Nombres de Bordeaux 24.3 (2012): 773-781. <http://eudml.org/doc/251129>.

@article{Zorin2012,
abstract = {We establish a new multiplicity lemma for solutions of a differential system extending Ramanujan’s classical differential relations. This result can be useful in the study of arithmetic properties of values of Riemann zeta function at odd positive integers (Nesterenko, 2011).},
affiliation = {Department of Mathematics University of York York, YO10 5DD, UK},
author = {Zorin, Evgeniy},
journal = {Journal de Théorie des Nombres de Bordeaux},
language = {eng},
month = {11},
number = {3},
pages = {773-781},
publisher = {Société Arithmétique de Bordeaux},
title = {Multiplicity estimate for solutions of extended Ramanujan’s system},
url = {http://eudml.org/doc/251129},
volume = {24},
year = {2012},
}

TY - JOUR
AU - Zorin, Evgeniy
TI - Multiplicity estimate for solutions of extended Ramanujan’s system
JO - Journal de Théorie des Nombres de Bordeaux
DA - 2012/11//
PB - Société Arithmétique de Bordeaux
VL - 24
IS - 3
SP - 773
EP - 781
AB - We establish a new multiplicity lemma for solutions of a differential system extending Ramanujan’s classical differential relations. This result can be useful in the study of arithmetic properties of values of Riemann zeta function at odd positive integers (Nesterenko, 2011).
LA - eng
UR - http://eudml.org/doc/251129
ER -

References

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  1. P. Kozlov, On algebraic independence of functions from a certain class. Izvestiya: Mathematics (Izvestiya of the Russian Academy of Sciences, in russian), in press. Zbl1272.11090
  2. Yu. Nesterenko, Modular functions and transcendence questions. Math. Sb. 187/9 (1996), 65–96 (Russian); English translation in Sb. Math. 187/9, 1319–1348. Zbl0898.11031MR1422383
  3. Yu. Nesterenko, Some identities of Ramanujan type. Moscow Journal of Combinatorics and Number Theory, Vol. 1 (2011), issue 2. Zbl1302.11051
  4. Yu. Nesterenko, Patrice Philippon (eds.), Introduction to Algebraic Independence Theory. Lecture Notes in Mathematics, Vol. 1752, Springer, 2001. Zbl0966.11032MR1837822
  5. F. Pellarin, La structure différentielle de l’anneau des formes quasi-modulaires pour SL 2 ( ℤ ) . Journal de Théorie des Nombres de Bordeaux 18, no.1 (2006), 241–264. Zbl1120.11022MR2245884
  6. P. Philippon, Indépendance algébrique et K -fonctions. J. reine angew. Math. 497 (1998), 1–15. Zbl0887.11032MR1617424
  7. P. Philippon, Une approche méthodique pour la transcendance et l’indépendance algébrique de valeurs de fonctions analytiques. J. Number Theory 64 (1997), 291–338. Zbl0901.11026MR1453214
  8. J.-P. Serre, A Course in Arithmetic. Springer-Verlag, New York, 1973. Zbl0432.10001MR344216
  9. E. Zorin, Lemmes de zéros et relations fonctionnelles. Thèse de doctorat de l’Université Paris 6, 2010. Accessible at http://tel.archives-ouvertes.fr/tel-00558073/fr/ 

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