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## Small gaps between prime numbers: The work of Goldston-Pintz-Yildirim

- K. Soundararajan
- Mathematics
- 27 May 2006

In early 2005, Dan Goldston, Janos Pintz, and Cem Yildirim [12] made a spectacular breakthrough in the study of prime numbers. Resolving a long-standing open problem, they proved that there are… Expand

## Divisibility of Class Numbers of Imaginary Quadratic Fields

- K. Soundararajan
- Mathematics
- 1 June 2000

Let d be a square‐free number and let CL(−d) denote the ideal class group of the imaginary quadratic number field Q(√−d). Further let h(−d) = #CL(−d) denote the class number. For integers g ⩾ 2, we… Expand

## Bounding |ζ(½+it)| on the Riemann hypothesis

- Vorrapan Chandee, K. Soundararajan
- Mathematics
- 14 August 2009

In 1924 Littlewood showed that, assuming the Riemann hypothesis, for large t, there is a constant C such that |ζ(1/2+it)|≪exp(Clog t/log log t). In this note we show how the problem of bounding… Expand

## Strong Multiplicity One for the Selberg Class

- K. Soundararajan
- MathematicsCanadian Mathematical Bulletin
- 18 October 2002

Abstract We investigate the problem of determining elements in the Selberg class by means of their Dirichlet series coefficients at primes.

## A model problem for multiplicative chaos in number theory

- K. Soundararajan, Asif Zaman
- MathematicsL’Enseignement Mathématique
- 16 August 2021

. Resolving a conjecture of Helson, Harper recently established that partial sums of random multiplicative functions typically exhibit more than square-root cancellation. Harper’s work gives an… Expand

## Exponential sums, twisted multiplicativity and moments

- E. Kowalski, K. Soundararajan
- Mathematics
- 14 July 2021

. We study averages over squarefree moduli of the size of exponential sums with polynomial phases. We prove upper bounds on various moments of such sums, and obtain evidence of un-correlation of… Expand

## Quantum Unique Ergodicity and Number Theory

- K. Soundararajan
- Mathematics
- 1 June 2011

A fundamental problem in the area of quantum chaos is to understand the distribution of high eigenvalue eigenfunctions of the Laplacian on certain Riemannian manifolds. A particular case which is of… Expand

## The distribution of values of zeta and L-functions

- K. Soundararajan
- Mathematics
- 6 December 2021

This article concerns the distribution of values of the Riemann zeta-function, and related L-functions. We begin with a brief discussion of L-values at the edge of the critical strip, which give… Expand

## A ug 2 00 5 NEGATIVE VALUES OF TRUNCATIONS TO L ( 1 , χ )

- A. Granville, K. Soundararajan
- Mathematics
- 2022

∑ n≤x λ(n) is non-positive for all x ≥ 2, which also implies the Riemann Hypothesis). In [4] Haselgrove showed that both the Turán and Pólya conjectures are false; therefore we know that truncations… Expand

## N T ] 1 J un 2 00 6 SIEVING AND THE ERDŐS-KAC THEOREM

- A. Granville, K. Soundararajan
- Mathematics
- 2018

It is natural to ask how ω(n) is distributed as one varies over the integers n ≤ x. A famous result of Hardy and Ramanujan [13] tells us that ω(n) ∼ log log x for almost all n ≤ x; we say that ω(n)… Expand

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