Alex Cowan

collaborators

4 papers

math.NT2025

On the mean value of $GL_{1}$ and $GL_{2}$ $L$ -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 $L$ -functions. The root cause of this phenomenon remains…

math.NT2025

The relative entropy of primes in arithmetic progressions is really small

Alex Cowan

Fix a modulus $q$ . One would expect the number of primes in each invertible residue class mod $q$ to be multinomially distributed, i.e. for each $p mod q$ to behave li…

math.NT2025

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…

math.NT2025

Conductor distributions of elliptic curves

Alex Cowan

We determine the distribution of the conductors $N$ of rational elliptic curves when ordered by naive height $H$ , in the form of an explicit density function for the ratios $N / H$ .…

On the mean value of GL1​ and GL2​ L-functions, with applications to murmurations

The relative entropy of primes in arithmetic progressions is really small

Murmurations and ratios conjectures

Conductor distributions of elliptic curves

On the mean value of $GL_{1}$ and $GL_{2}$ $L$ -functions, with applications to murmurations