Verifying Harder's Conjecture for Classical and Siegel Modular Forms

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.

Public Speaking Anxiety, Test Anxiety, and Academic Achievement in Undergraduate Students

Public speaking anxiety and test anxiety are both psychological difficulties which may adversely influence academic achievement in undergraduate students. Previous research has indicated that both public speaking anxiety and test anxiety are negatively correlated with academic performance, usually measured by grade point average. The purpose of this study was to assess the prevalence of public speaking anxiety, test anxiety, and their effects on academic achievement in a sample of undergraduate students, and to determine if certain groups of students are more likely to be affected than others. Although test anxiety and public speaking anxiety were both found to be negatively correlated with grade point average, these correlations were not statistically significant. Potential reasons for the lack of statistical congruence with previous studies, as well as implications for future research and treatment, are discussed.