This cluster revolves around advanced mathematical topics. It includes a question on the proof of Cayley’s Theorem for Topological Groups and another related to the analytic continuation of a complex function involving the sinc function and the polylogarithm function, and includes the digamma function too. The use of topological groups and integral representations of functions makes these problems relevant to the field of mathematical analysis and abstract algebra.
This cluster focuses on mathematical concepts and problems, specifically involving integral regularization, Green’s functions, and Diophantine equations. The discussion includes the regularization of a contour integral using complex analysis, the asymptotics of Green functions near the diagonal, and an unsolved Diophantine equation. These topics represent core areas of pure mathematics and analytical techniques.