1 citations · 3 across the 12 of their papers we have counts for
13 papers
The relative entropy of primes in arithmetic progressions is really small
Alex Cowan
Fix a modulus . One would expect the number of primes in each invertible residue class mod to be multinomially distributed, i.e. for each to behave li…
On the mean value of and -functions, with applications to murmurations
Alex Cowan
"Murmurations" are a recently-discovered type of fine structure in sums of Dirichlet coefficients averaged over families of -functions. The root cause of this phenomenon remains…
Murmurations and ratios conjectures
Alex Cowan
We introduce a new method for studying murmurations, based on random matrix theory. With this method, we exhibit murmurations or similar phenomena: assuming ratios conjectures, for…
Conductor distributions of elliptic curves
Alex Cowan
We determine the distribution of the conductors of rational elliptic curves when ordered by naive height , in the form of an explicit density function for the ratios .…
Murmurations and explicit formulas
Alex Cowan
Unexpected oscillations in values in a family of elliptic curves were observed experimentally by He, Lee, Oliver, and Pozdnyakov. We propose a heuristic explanation for these…
A twisted additive divisor problem
Alex Cowan
We give asymptotics for shifted convolutions of the form for nonzero complex numbers and nontrivial Dirichlet charac…
Counting modular forms by rationality field
Alex Cowan, Kimball Martin
We investigate the distribution of degrees and rationality fields of weight 2 newforms. In particular, we give heuristic upper bounds on how often degree rationality fields occ…
Moduli for rational genus 2 curves with real multiplication for discriminant 5
Alex Cowan, Kimball Martin
Principally polarized abelian surfaces with prescribed real multiplication (RM) are parametrized by certain Hilbert modular surfaces. Thus rational genus 2 curves correspond to rat…
Computing newforms using supersingular isogeny graphs
Alex Cowan
We describe an algorithm that we used to compute the q-expansions of all weight 2 cusp forms of prime level at most 2,000,000 and dimension at most 6. We also present an algorithm…
Conjecture: 100% of elliptic surfaces over have rank zero
Alex Cowan
Based on an equation for the rank of an elliptic surface over which appears in the work of Nagao, Rosen, and Silverman, we conjecture that 100% of elliptic surfaces ha…
Non-Random Behaviour in Sums of Modular Symbols
Alexander Cowan
We give explicit expressions for the Fourier coefficients of Eisenstein series twisted by Dirichlet characters and modular symbols on in the case where is prime and eq…
The distribution of multiples of real points on an elliptic curve
Alex Cowan
Given an elliptic curve and a point in , we investigate the distribution of the points as varies over the integers, giving bounds on the and …
Constants in Titchmarsh divisor problems for elliptic curves
Renee Bell, Clifford Blakestad, Alina Carmen Cojocaru +5
Inspired by the analogy between the group of units of the finite field with elements and the group of points of an elliptic curve $E/\…