Tohoku Mathematical Journal
2013
June
SECOND SERIES VOL. 65, NO. 2

Tohoku Math. J.
65 (2013), 159-178

Title MEROMORPHIC CONTINUATIONS OF LOCAL ZETA FUNCTIONS AND THEIR APPLICATIONS TO OSCILLATING INTEGRALS

Author Toshihisa Okada and Kiyoshi Takeuchi

(Received November 17, 2011, revised July 13, 2012)
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.

Mathematics Subject Classification. Primary 14B05; Secondary 14M25, 14N99, 52B20.
Key words and phrases. Local zeta function, toric variety, oscillating integral.

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