24 citations · 79 across the 17 of their papers we have counts for
5 papers · 1 filter
Moments of the Riemann zeta-function
K. Soundararajan
Assuming the Riemann Hypothesis we obtain an upper bound for the moments of the Riemann zeta-function on the critical line. Our bound is nearly as sharp as the conjectured asymptot…
Pretentious multiplicative functions and an inequality for the zeta-function
Andrew Granville, K. Soundararajan
We note how several central results in multiplicative number theory may be rephrased naturally in terms of multiplicative functions that pretend to be another multiplicative fu…
Sieving and the Erd{\H o}s-Kac theorem
Andrew Granville, K. Soundararajan
We give a relatively easy proof of the Erd\H os-Kac theorem via computing moments. We show how this proof extends naturally in a sieve theory context, and how it leads to several r…
Two -unit equations with many solutions
S. Konyagin, K. Soundararajan
We show that there exist arbitrarily large sets of prime numbers such that the equation has more than solutions in coprime integers , $b…
Lower bounds for moments of L-functions: symplectic and orthogonal examples
Z. Rudnick, K. Soundararajan
We give lower bounds of the conjectured order of magnitude for an orthogonal and a symplectic family of L-functions.