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- W1967423737 abstract "Let f(x) be a polynomial with p-adic coefficients, and defineS(f;χ;Z/pmZ)=∑x∈(Z/pmZ)×χ(x)e2πif(x)/pm, where χ is a character of (Z/pmZ)×. For example, f(x)=x leads to the Gauss sum of χ. An explicit formula for S(f;χ;Z:/pmZ) is given if f′(x) has distinct roots in Z/pmZ and m⩾2, or if f′(x) has distinct roots p-adically and m is sufficiently large. In either case, the formula involves one term for each root of f′(x). If the derivative does not have distinct roots, there is a less explicit formula, requiring one term for each approximate root. Analogous results are proved for sums involving several variables. As applications of these results, Mauclaire's evaluation of the Gauss sum is re-derived, and new results on n-variable Kloosterman sums are obtained." @default.
- W1967423737 created "2016-06-24" @default.
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- W1967423737 date "2002-09-01" @default.
- W1967423737 modified "2023-10-18" @default.
- W1967423737 title "The Stationary-Phase Method for Exponential Sums with Multiplicative Characters" @default.
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- W1967423737 doi "https://doi.org/10.1006/jnth.2002.2790" @default.
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