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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

Poles of a two-variable $ P$-adic complex power


Author: Leon Strauss
Journal: Trans. Amer. Math. Soc. 278 (1983), 481-493
MSC: Primary 14G20; Secondary 12B30, 12B40
MathSciNet review: 701506
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Abstract: For almost all $ P$-adic completions of an algebraic number field, if $ s \in {\mathbf{C}}$ is a pole of $ {f^s} = \int_{}^{} {\int_{}^{} {\vert f(x,y){\vert^s}\vert dx{\vert _{{K_p}}}\vert dy{\vert _{{K_p}}}} } $ , where $ f$ is a polynomial whose only singular point is the origin, $ f(0,0) = 0$, and $ f$ is irreducible in $ \overline K [[x,y]]$, then $ \operatorname{Re} (s)$ is $ - 1$ or one of an explicitly given set of rational numbers, whose cardinality is the number of characteristic exponents of $ f = 0$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1983-0701506-2
PII: S 0002-9947(1983)0701506-2
Article copyright: © Copyright 1983 American Mathematical Society