This thesis investigates the spectral instabilities of various nonlinear water wave models through rigorous analytical techniques. Focusing on three fundamental types of instabilities, modulational instability, transverse ...

Summation formulas play a vital role in analytic number theory. Several kinds of summation formulas exist, like the Poisson summation formula, Abel summation formula, Euler-Maclaurin formula, etc. In 1904, G. F. Voronoi ...