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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 topological interpretation to a certain induced representation. It also explains how the discrete Fourier transform can be related to 3- and 4-dimensional topology. Theta Functions and Knots can be read in two perspectives. People with an interest in theta functions or knot theory can learn how the two are related. Those intere

Functions, Theta. --- Knot theory. --- Knots (Topology) --- Low-dimensional topology --- Theta functions

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Theta functions were studied extensively by Ramanujan. This book provides a systematic development of Ramanujan’s results and extends them to a general theory. The author’s treatment of the subject is comprehensive, providing a detailed study of theta functions and modular forms for levels up to 12. Aimed at advanced undergraduates, graduate students, and researchers, the organization, user-friendly presentation, and rich source of examples, lends this book to serve as a useful reference, a pedagogical tool, and a stimulus for further research. Topics, especially those discussed in the second half of the book, have been the subject of much recent research; many of which are appearing in book form for the first time. Further results are summarized in the numerous exercises at the end of each chapter.

Mathematics. --- Algebraic geometry. --- Number theory. --- Number Theory. --- Algebraic Geometry. --- Functions, Theta. --- Theta functions --- Geometry, algebraic. --- Algebraic geometry --- Geometry --- Number study --- Numbers, Theory of --- Algebra

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Ordered algebraic structures --- 511.9 --- Geometry of numbers --- 511.9 Geometry of numbers --- Functions, Theta --- Modular groups --- Riemann surfaces --- Surfaces, Riemann --- Functions --- Group theory --- Matrices --- Number theory --- Theta functions

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Number theory --- 51 <082.1> --- Mathematics--Series --- Number theory. --- Combinatorial identities. --- Functions, Theta. --- Generating functions. --- Partitions (Mathematics) --- Nombres, Théorie des. --- Identités combinatoires. --- Fonctions thêta. --- Fonctions génératrices. --- Partitions (mathématiques) --- Combinatorial identities --- Functions, Theta --- Generating functions --- Number study --- Numbers, Theory of --- Algebra --- Functions, Generating --- Combinatorial analysis --- Theta functions --- Identities, Combinatorial --- Identités combinatoires .

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Algebraic geometry --- Ordered algebraic structures --- Curves, Algebraic --- Functions, Theta --- Jacobi varieties --- 512.77 --- #TCPW W5.0 --- #WWIS:d.d. Prof. L. Bouckaert/ALTO --- Varieties, Jacobi --- Riemann surfaces --- Algebraic curves --- Algebraic varieties --- Theta functions --- Algebraic curves. Algebraic surfaces. Three-dimensional algebraic varieties --- 512.77 Algebraic curves. Algebraic surfaces. Three-dimensional algebraic varieties