Resolution of singularities, asymptotic expansions of oscillatory integrals, and related phenomena

2007/09/16 by Michael Greenblatt, Greenblatt, Michael · 1 citation
Mathematics · #Algebraic and Geometric Analysis #Mathematical functions and polynomials #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.0709.2496

Abstract

The elementary resolution of singularities algorithm of the author's earlier paper (math.CA/0609217) is developed further, replacing the quasibump functions in the blown up coordinates with the characteristic function of a rectangle times a smooth function. Such functions are easier to deal with, and as application the existence of asymptotic expansions for oscillatory integrals and related objects is given an elementary proof. In addition, some more detailed information about these expansions is given.

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• Applications of an elementary resolution of singularities algorithm to\n exponential sums and congruences modulo pⁿ

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