7 papers
Murmurations in the depth aspect
Claire Burrin, Vivian Kuperberg, Min Lee +2
We compute the murmuration density function for the family of Hecke forms of weight and prime power level , with a fixed odd prime and .
Odd moments and adding fractions
Thomas F. Bloom, Vivian Kuperberg
We prove near-optimal upper bounds for the odd moments of the distribution of coprime residues in short intervals, confirming a conjecture of Montgomery and Vaughan. As an applicat…
The gaps in the multiplication table
Emmanuel Kowalski, Vivian Kuperberg
We determine the complete list of the gaps between successive elements of the multiplication table of the first N integers.
Distributions of left prime truncations
Vivian Kuperberg, Matilde LalÃn
The prime number 357686312646216567629137 is notable because of the unusual property that it remains prime successively on removing the left digit until there are no remaining digi…
Statistics of ranks, determinants and characteristic polynomials of rational matrices
Muhammad Afifurrahman, Vivian Kuperberg, Alina Ostafe +1
We consider the set of matrices with rational entries having numerator and denominator of size at most and obtain upper and lower bounds on the number of such matri…
Positive density for consecutive runs of sums of two squares
Noam Kimmel, Vivian Kuperberg
We study the distribution of consecutive sums of two squares in arithmetic progressions. We show that for any odd squarefree modulus , any two reduced congruence classes a…