Date of Thesis
A conjecture by Harder shows a surprising congruence between the coefficients of “classical” modular forms and the Hecke eigenvalues of corresponding Siegel modular forms, contigent upon “large primes” dividing the critical values of the given classical modular form.
Harder’s Conjecture has already been verified for one-dimensional spaces of classical and Siegel modular forms (along with some two-dimensional cases), and for primes p 37. We verify the conjecture for higher-dimensional spaces, and up to a comparable prime p.
Modular Forms, Siegel Modular Forms, Congruence, Harder, Critical Values, Large Primes, Hecke Eigenvalues
Nathan C. Ryan
Sulon, David, "Verifying Harder's Conjecture for Classical and Siegel Modular Forms" (2012). Honors Theses. 98.