1 citations · 2 across the 10 of their papers we have counts for
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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…