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math.NT2024
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.NT2024
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 .…