Kannan Soundararajan

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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)
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)
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)
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)