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There are connections between invariant theory and modular forms
since the times of Felix Klein, in the 19th century, connections
between codes and lattices since the 1960's. The aim of the book is
to explore the interplay between codes and modular forms. Here
modular form is understood in a wide sense (Jacobi forms, Siegel
forms, Hilbert forms). Codes comprises not only linear spaces over
finite fields but modules over some commutative rings. The
connection between codes over finite fields and lattices has been
well documented since the 1970s. Due to an avalanche of results on
codes over rings since the 1990's there is a need for an update at
book level.
This book explores various properties of quasimodular forms,
especially their connections with Jacobi-like forms and automorphic
pseudodifferential operators. The material that is essential to the
subject is presented in sufficient detail, including necessary
background on pseudodifferential operators, Lie algebras, etc., to
make it accessible also to non-specialists. The book also covers a
sufficiently broad range of illustrations of how the main themes of
the book have occurred in various parts of mathematics to make it
attractive to a wider audience. The book is intended for
researchers and graduate students in number theory.
This book explores various properties of quasimodular forms,
especially their connections with Jacobi-like forms and automorphic
pseudodifferential operators. The material that is essential to the
subject is presented in sufficient detail, including necessary
background on pseudodifferential operators, Lie algebras, etc., to
make it accessible also to non-specialists. The book also covers a
sufficiently broad range of illustrations of how the main themes of
the book have occurred in various parts of mathematics to make it
attractive to a wider audience. The book is intended for
researchers and graduate students in number theory.
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