14 citations · 36 across the 7 of their papers we have counts for
7 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…
The fourth moment of Dirichlet -functions
K. Soundararajan
Extending a result of Heath-Brown, we establish an asymptotic formula for the fourth moment of central values of Dirichlet -functions attached to primitive characters .
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…
Approximating 1 from below using Egyptian fractions
K. Soundararajan
We find the closest approximation to 1 from below using a sum of Egyptian fractions.
Extreme values of
Andrew Granville, K. Soundararajan
Improving a result of N. Levinson, we exhibit large and small values 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…