Explicit analytic functions defining the images of wave-front singularities

Kentaro Saji; Masaaki Umehara; Kotaro Yamada

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arXiv · 2512.21518

Explicit analytic functions defining the images of wave-front singularities

Kentaro Saji·Masaaki Umehara·Kotaro Yamada

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Abstract

We give explicit real-analytic functions whose zero sets characterize the images of the standard maps of wave-front singularities. Such functions are realizations of the main-analytic sets in the sense of Ishikawa-Koike-Shiota (1984). More concretely, a subset of Euclidean space is called a global main-analytic set if it can be described, up to a set of smaller Hausdorff dimension, as part of the zero set of a single real-analytic function, referred to as its main-analytic function. In this paper, we propose a general framework for constructing main-analytic functions by a method based on explicit resultant computations. In particular, we provide explicit formulas for the main-analytic functions associated with the standard maps of wave-front singularities of types A, D and E.

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Kentaro Saji, Masaaki Umehara, Kotaro Yamada. 2025-12-25. Explicit analytic functions defining the images of wave-front singularities. https://arxiv.org/abs/2512.21518

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