There are incredibly rich connections between classical analysis and number theory. For instance, analytic number theory contains many examples of asymptotic expressions derived from estimates for analytic functions, such as in the proof of the Prime Number Theorem. In combinato…
This book presents the relationship between classical theta functions and knots. It is based on a novel idea of Razvan Gelca and Alejandro Uribe, which converts Weil's representation of the Heisenberg group on theta functions to a knot theoretical framework, by giving a topologi…
These notes present new as well as classical results from the theory of theta functions on Riemann surfaces, a subject of renewed interest in recent years. Topics discussed here include: the relations between theta functions and Abelian differentials, theta functions on degenera…
These notes present new as well as classical results from the theory of theta functions on Riemann surfaces, a subject of renewed interest in recent years. Topics discussed here include: the relations between theta functions and Abelian differentials, theta functions on degenera…
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This is an advanced book on modular forms. While there are many books published about modular forms, they are written at an elementary level, and not so interesting from the viewpoint of a reader who already knows the℗ basics. This book offers something new, which may satisfy th…
