Periodic Functions: Self-Intersection and Local Singular Points

Self-intersections and local singular points of the curves play an important role in algebraic geometry and many other areas. In the present paper, we study the self-intersection and local singular points of the n-member chains. For this purpose, we derive and use several new results on trigonometric formulas. A unified approach for calculating self-intersection and local singular points for a wide class of curves is presented. An application to the spectral theory of integro-differential operators with difference kernels is given as well.