We study planar domains with exemplary boundary singularities of the form cusps. A natural question is how much elastic energy needed to flatten these cusps; that is, remove singularities. give, in a connection quasidisks, sharp integrability condition for distortion function answer this question.

In this note, we propose a new construction of cyclotomic p-adic L-functions that are attached to classical modular cuspidal eigenforms. This allows for us cover most known cases date and provides method which is amenable generalizations automorphic forms on arbitrary groups. the setting GL2 over Q, construct L-function in so far uncovered extremal case, arises under unlikely hypothesis p-th He...