Tohoku Mathematical Journal

Meromorphic continuations of local zeta functions and their applications to oscillating integrals

Toshihisa Okada and Kiyoshi Takeuchi

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Abstract

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.

Article information

Source
Tohoku Math. J. (2), Volume 65, Number 2 (2013), 159-178.

Dates
First available in Project Euclid: 25 June 2013

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1372182720

Digital Object Identifier
doi:10.2748/tmj/1372182720

Mathematical Reviews number (MathSciNet)
MR3079283

Zentralblatt MATH identifier
1345.14010

Subjects
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]

Keywords
Local zeta function toric variety oscillating integral

Citation

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


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