46 citations · 144 across the 14 of their papers we have counts for
13 papers · 1 filter
The least quadratic residue and integers represented by quadratic forms
Kannan Soundararajan, João C. C. Vargas
Let denote the least non-trivial reduced quadratic residue modulo ; that is, denotes the smallest square-free integer with and $r\equiv x^2 \…
Distribution of random multiplicative functions in short intervals, with proper normalization
Adam J. Harper, Kannan Soundararajan, Max Wenqiang Xu
We determine the limiting distribution of partial sums of a Steinhaus random multiplicative function over short intervals , where $y \rightar…
Covering integers by
Ben Green, Kannan Soundararajan
What proportion of integers may be expressed as for some , with integers? Writing as $(\log N)^{\log 2} 2^{α\sqrt{\log \log N…
On short sums of trace functions
É. Fouvry, E. Kowalski, Ph. Michel +3
We consider sums of oscillating functions on intervals in cyclic groups of size close to the square root of the size of the group. We first prove non-trivial estimates for interval…
Small gaps between zeros of twisted L-functions
J. B. Conrey, H. Iwaniec, K. Soundararajan
We use the asymptotic large sieve, developed by the authors, to prove that if the Generalized Riemann Hypothesis is true, then there exist many Dirichlet L-functions that have a pa…
The Prime Geodesic Theorem
K. Soundararajan, Matthew P. Young
We study the distribution of closed geodesics for the modular surface. We improve the error term in the prime geodesic theorem, and obtain results on prime geodesics in very short…
Mass equidistribution for Hecke eigenforms
R. Holowinsky, K. Soundararajan
We prove a conjecture of Rudnick and Sarnak on the mass equidistribution of Hecke eigenforms. This builds upon independent work of the authors see arxiv.org:math/0809.1640 and arxi…
Weak subconvexity for central values of -functions
K. Soundararajan
We describe a general method to obtain weak subconvexity bounds for many classes of -functions. This has applications to a conjecture of Rudnick and Sarnak for the mass equidist…
Partial sums of the M{ö}bius function
K. Soundararajan
Assuming the Riemann Hypothesis we establish an upper bound for the sum of the M{\" o}bius function up to . Our method is based on estimating the frequency with which intervals…
Benford's law for the function
Jeffrey C. Lagarias, K. Soundararajan
We show that for most choices of an initial seed , the sequence of the first iterates of under the map approximately satisfies Benford's law.
Real zeros of quadratic Dirichlet L-functions
J. Brian Conrey, Kannan Soundararajan
We show that for a positive proportion of real primitive Dirichlet characters chi, the associated Dirichlet L-function L(s,chi) has no zeros on the positive real axis. Prior to thi…
Beyond pair correlation
Hugh L. Montgomery, K. Soundararajan
The authors study the distribution of psi(x+h)-psi(x)-h and compare it with numerical data.
Transition mean values of real characters
J. Brian Conrey, David W. Farmer, K. Soundararajan
We evaluate the character sum sigma_m sigma_n (m/n) where the two sums are of approximately the same length. The answer is surprising.