We present a different version of the well-known connection between Hopf–Galois structures and skew braces, building on recent paper A. Koch P. J. Truman. show that known results involve this easily carry over to new perspective, ones naturally appear. As an application, we insights study surjectivity correspondence, explaining in more detail role bi-skew braces theory.

We investigate the behaviour of orthogonal non-holomorphic Eisenstein series at their harmonic points by using theta lifts. In case singular weight, we show that can be written as a lift have simple pole $s = 1$ whose residues yield holomorphic modular forms are on boundary and give sufficient condition surjectivity this construction.