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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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On the Poincaré series for diagonal forms
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by Jun Wang
Proc. Amer. Math. Soc. 116 (1992), 607-611
DOI: https://doi.org/10.1090/S0002-9939-1992-1116274-3

Abstract:

Let $p$ be a fixed prime, $f({x_1}, \ldots ,{x_s})$ a polynomial over ${{\mathbf {Z}}_p}$, the $p$-adic integers, ${c_n}$ the number of solutions of $f = 0$ over ${\mathbf {Z}}/{p^n}{\mathbf {Z}}$, and ${P_f}(t) = \sum \nolimits _{n = 0}^\infty {{c_n}{t^n}}$ the Poincaré series. Explicit formulas for ${P_f}(t)$ are derived for diagonal forms.
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Bibliographic Information
  • © Copyright 1992 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 116 (1992), 607-611
  • MSC: Primary 11E95; Secondary 11D88, 11E76, 11L03
  • DOI: https://doi.org/10.1090/S0002-9939-1992-1116274-3
  • MathSciNet review: 1116274