Pseudodifferential Methods in Number Theory

The book "Pseudodifferential Methods in Number Theory" offers an innovative perspective on the application of pseudodifferential methods in number theory. Originally developed as a tool for analyzing partial differential equations, pseudodifferential analysis is here considered as a potential aid in solving arithmetic problems. The operators discussed in the book are characterized by congruence arithmetic properties and exhibit an Eulerian structure. These operators are used to find new conditions that are equivalent to the Riemann Hypothesis and include the validity of certain parameter-dependent estimates for a class of finite-rank Hermitian forms. The book is aimed at readers interested in new approaches to the Riemann Hypothesis, as well as those seeking new perspectives on pseudodifferential analysis and its connection to modular form theory. The analytical aspects are easily understandable for professionals, and extensive prior knowledge in arithmetic is not required.