Alladi Ramakrishnan Hall

$q$ -product expansions of modular functions

Winfried Kohnen

University of Heidelberg

Modular functions not only have Fourier expansions, but also have $q$-product
expansions. Their exponents often are important to study, too relating to e.g., divisors
of modular functions, the existence of $\eta$-products, generalized modular forms and most
recently to representation numbers of integers as sums of arbitrarily many squares. I intend
to survey some of these topics