4 papers
math.NT2025
Counting newforms with prescribed ramified supercuspidal components
Andrew Knightly, Kimball Martin
We give a formula for the number of newforms in that have prescribed ramified supercuspidal components at a set of primes dividing . This dime…
math.NT2025
Distribution of local signs of modular forms and murmurations of Fourier coefficients
Kimball Martin
Recently, we showed that global root numbers of modular forms are biased toward +1. Together with Pharis, we also showed an initial bias of Fourier coefficients towards the sign of…
math.NT2025
Rationality fields of CM modular forms
Kimball Martin
We formulate a conjecture on the finitude of rationality fields (i.e., Fourier coefficient fields) of newforms of bounded degree, and prove this for CM forms assuming a generalized…
math.NT2025
Variations on murmurations
Kimball Martin
We explore several variations on the recently discovered phenomena of murmurations for elliptic curves and modular forms.