Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8896902 | Journal of Number Theory | 2018 | 17 Pages |
Abstract
We refine known dimension formulas for spaces of cusp forms of squarefree level, determining the dimension of subspaces generated by newforms both with prescribed global root numbers and with prescribed local signs of Atkin-Lehner operators. This yields precise results on the distribution of signs of global functional equations and sign patterns of Atkin-Lehner eigenvalues, refining and generalizing earlier results of Iwaniec, Luo and Sarnak. In particular, we exhibit a strict bias towards root number +1 and a phenomenon that sign patterns are biased in the weight but perfectly equidistributed in the level. Another consequence is lower bounds on the number of Galois orbits.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Kimball Martin,