Date of Thesis
2015
Description
We explore the attraction of zeros near the central point of L-functions associated with elliptic curves and modular forms. Specifically, we consider families of twists of elliptic curves, the family of weight 2 modular forms, and the family of level 1 modular forms. We observe experimentally an attraction of the zeros near the central point, and that the attraction decreases with the rank r of the L-function. However, for each set of L-functions of rank r within a particular family we observe a statistically significant increase in the attraction as the conductors of the L-functions increase. This indicates a correspondence with the random matrix theory result about the vanishing of the distance between eigenangles near 1 as the size of the matrix increases, but also that this correspondence only exists in the limit, since we observe less attraction otherwise. Additionally, we begin preliminary investigation on a new statistic, the relationship between the value of the first zero above the central point and the value of the L-function at s = 1/2.
Keywords
Random matrix theory, l-functions, Modular forms, Elliptic curves
Access Type
Honors Thesis
Degree Type
Bachelor of Science
Major
Mathematics
First Advisor
Nathan Ryan
Recommended Citation
Harris, Katherine Elizabeth, "Random Matrix Theory and the Attraction of Zeros of L-Functions From the Central Point" (2015). Honors Theses. 321.
https://digitalcommons.bucknell.edu/honors_theses/321