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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The multidimensional $p$-adic Green function
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by Nguyen Minh Chuong and Nguyen Van Co
Proc. Amer. Math. Soc. 127 (1999), 685-694
DOI: https://doi.org/10.1090/S0002-9939-99-04954-0
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Abstract:

A proof much simpler than the one given by Bikulov (Investigation of the $p$-adic Green function, Teoret. Mat. Fiz. 87 (1991), 376–390) for properties of the 2-dimensional $p$-adic Green function is shown. By this method one can treat a multidimensional case, and some sharp estimates are obtained.
References
  • A. Kh. Bikulov, Investigation of a $p$-adic Green function, Teoret. Mat. Fiz. 87 (1991), no. 3, 376–390 (Russian, with English summary); English transl., Theoret. and Math. Phys. 87 (1991), no. 3, 600–610. MR 1129672, DOI 10.1007/BF01017946
  • Nguyen Minh Chuong, Nguyen Van Co and Tran Quoc Binh, $p$-adic distributions and Sobolev spaces, Preprint 96/10, Hanoi Institute of Mathematics.
  • Nguyen Minh Chuong and Nguyen Van Co, A new proof for $p$-adic Green function, Preprint 1997, Hanoi Institute of Mathematics.
  • Nguyen Minh Chuong, Nguyen Minh Tri and Le Quang Trung, Theory of Partial Differential Equations, Sci. & Jechn. Publ. House, Hanoi (1995).
  • G. Christol and B. Dwork, Effective $p$-adic bounds at regular singular points, Duke Math. J. 62 (1991), no. 3, 689–720. MR 1104814, DOI 10.1215/S0012-7094-91-06230-7
  • Andrei Khrennikov, $p$-adic valued distributions in mathematical physics, Mathematics and its Applications, vol. 309, Kluwer Academic Publishers Group, Dordrecht, 1994. MR 1325924, DOI 10.1007/978-94-015-8356-5
  • Neal Koblitz, $p$-adic numbers, $p$-adic analysis, and zeta-functions, 2nd ed., Graduate Texts in Mathematics, vol. 58, Springer-Verlag, New York, 1984. MR 754003, DOI 10.1007/978-1-4612-1112-9
  • V. S. Vladimirov, I. V. Volovich, and E. I. Zelenov, $p$-adicheskiÄ­ analiz i matematicheskaya fizika, VO “Nauka”, Moscow, 1994 (Russian, with Russian summary). MR 1349578
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Bibliographic Information
  • Nguyen Minh Chuong
  • Affiliation: Hanoi Institute of Mathematics, P.O. Box 631 Boho, 10 000 Hanoi, Vietnam
  • Email: nmchuong@thevinh.ac.vn
  • Nguyen Van Co
  • Affiliation: Department Of Mathematics, Hanoi State University, Mai Dich, Tu Liem, Hanoi, Vietnam
  • Received by editor(s): July 1, 1997
  • Additional Notes: This paper was supported by the National Natural Science Foundation of Vietnam
  • Communicated by: Dennis A. Hejhal
  • © Copyright 1999 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 127 (1999), 685-694
  • MSC (1991): Primary 11S80; Secondary 81T99
  • DOI: https://doi.org/10.1090/S0002-9939-99-04954-0
  • MathSciNet review: 1618721