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
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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.References
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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