13 citations · 13 across the 6 of their papers we have counts for
8 papers
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 .
Prime Number Races
Andrew Granville, Greg Martin
This is a survey article on prime number races. Chebyshev noticed in the first half of the nineteenth century that for any given value of x, there always seem to be more primes of…
An uncertainty principle for arithmetic sequences
Andrew Granville, K. Soundararajan
Analytic number theorists usually seek to show that sequences which appear naturally in arithmetic are ``well-distributed'' in some appropriate sense. In various discrepancy proble…
The distribution of values of L(1,chi_d)
Andrew Granville, Kannan Soundararajan
In this paper we investigate the distribution of values of L(1,chi) as chi ranges over primitive real characters. In particular we focus on the extent to which this distribution ma…