Let K be a totally real number field of degree n. We show that the number of totally positive integers (or more generally the number of totally positive elements of a given fractional ideal) of given trace is evenly distributed around its expected value, which is obtained from geometric considerations. This result depends on unfolding an integral over a compact torus. Introduction In 1921 Hecke...

Studying the quadratic field theory on seven dimensional spacetime constructed by a direct product of Calabi-Yau three-fold by a real time axis, with phase space being the third cohomology of the Calabi-Yau three-fold, the generators of translation along moduli directions of Calabi-Yau three-fold are constructed. The algebra of these generators is derived which take a simple form in canonical c...

Linear quadratic graphon field games (LQ-GFGs) are defined to be LQ which involve a large number of agents that weakly coupled via weighted undirected graph on each node represents an agent. The links the correspond couplings between agents' dynamics, as well individual cost functions, agent attempts minimize. We formulate limit LQ-GFG problems based assumption these graphs lie in sequence conv...