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- K Soundararajan
- 2008

The moments of central values of families of L-functions have recently attracted much attention and, with the work of Keating and Snaith [(2000) Commun. Math. Phys. 214, 57-89 and 91-110], there are now precise conjectures for their limiting values. We develop a simple method to establish lower bounds of the conjectured order of magnitude for several such… (More)

- Ken Ono, K Soundararajan
- 2004

- K Soundararajan
- 2003

- Andrew Granville, K Soundararajan
- 2008

- Hugh L Montgomery, K Soundararajan
- 2008

Contrary to what would be predicted on the basis of Cramér's model concerning the distribution of prime numbers, we develop evidence that the distribution of ψ(x + H) − Cramér [4] modeled the distribution of prime numbers by independent random variables X n (for n ≥ 3) that take the value 1 (n is " prime ") with probability 1/ log n and take the value 0 (n… (More)

- Andrew Granville, K Soundararajan
- 2007

Dedicated to Richard Guy on his 80th birthday, for all the inspiring problems that he has posed Contents 1 Introduction: Deenitions and properties of the spectrum 2 The natural and logarithmic densities of m-th power residues 2a The proportion of m-th power residues up to x 2b Logarithmic proportions of m-th power residues 3 Basic properties of integral… (More)

- K Soundararajan
- 2000

- Andrew Granville, K Soundararajan
- 2006

- Andrew Granville, K Soundararajan
- 2006

Analytic number theorists usually seek to show that sequences which appear naturally in arithmetic are " well-distributed " in some appropriate sense. In various discrepancy problems, combinatorics researchers have analyzed limitations to equi-distribution, as have Fourier analysts when working with the " uncertainty principle ". In this article we find… (More)