Tohoku Mathematical Journal
- Tohoku Math. J. (2)
- Volume 65, Number 2 (2013), 159-178.
Meromorphic continuations of local zeta functions and their applications to oscillating integrals
We introduce a new method which enables us to calculate the coefficients of the poles of local zeta functions very precisely and prove some explicit formulas. Some vanishing theorems for the candidate poles of local zeta functions will be also given. Moreover we apply our method to oscillating integrals and obtain an explicit formula for the coefficients of their asymptotic expansions.
Tohoku Math. J. (2), Volume 65, Number 2 (2013), 159-178.
First available in Project Euclid: 25 June 2013
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Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 14B05: Singularities [See also 14E15, 14H20, 14J17, 32Sxx, 58Kxx]
Secondary: 14M25: Toric varieties, Newton polyhedra [See also 52B20] 14N99: None of the above, but in this section 52B20: Lattice polytopes (including relations with commutative algebra and algebraic geometry) [See also 06A11, 13F20, 13Hxx]
Okada, Toshihisa; Takeuchi, Kiyoshi. Meromorphic continuations of local zeta functions and their applications to oscillating integrals. Tohoku Math. J. (2) 65 (2013), no. 2, 159--178. doi:10.2748/tmj/1372182720. https://projecteuclid.org/euclid.tmj/1372182720