Numbers of solutions of congruences: Poincaré series for strongly nondegenerate forms
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- by Jay R. Goldman PDF
- Proc. Amer. Math. Soc. 87 (1983), 586-590 Request permission
Abstract:
Let $p$ be a fixed prime, $f({x_1}, \ldots ,{x_k})$ 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 ${P_f}(t) = \sum \nolimits _{i = 0}^\infty {{c_i}{t^i}}$ the Poincaré series. A general approach to computing ${c_n}$ and ${P_f}(t)$ is given and explicit formulas are derived for strongly nondegenerate forms.References
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Additional Information
- © Copyright 1983 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 87 (1983), 586-590
- MSC: Primary 11T99; Secondary 11E45, 11E76
- DOI: https://doi.org/10.1090/S0002-9939-1983-0687622-8
- MathSciNet review: 687622