14 citations · 39 across the 10 of their papers we have counts for
11 papers · 1 filter
The number of imaginary quadratic fields with a given class number
K. Soundararajan
We investigate the number ${\Cal F}(h)$ of imaginary quadratic fields with class number . We establish an asymptotic formula for the average value of ${\Cal F}(h)$. We also esta…
The distribution of smooth numbers in arithmetic progressions
K. Soundararajan
For a wide range of and we show that ${\Cal S}(x,y)$, the set of integers below composed only of prime factors below , is equidistributed in the reduced residue clas…
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…
Negative values of truncations to
Andrew Granville, K. Soundararajan
For a given we consider the minimum of as ranges over all quadratic Dirichlet characters. For all large , this minimum is negative and we give upp…
Large character sums: Pretentious characters and the Polya-Vinogradov Theorem
Andrew Granville, K. Soundararajan
In 1918 Polya and Vinogradov gave an upper bound for the maximal size of character sums which still remains the best known general estimate. One of the main results of this paper p…
Extreme values of
Andrew Granville, K. Soundararajan
Improving a result of N. Levinson, we exhibit large and small values of .