• Corpus ID: 119143467

The distribution of values of L(1,chi_d)

  title={The distribution of values of L(1,chi\_d)},
  author={Andrew Granville and Kannan Soundararajan},
  journal={arXiv: Number Theory},
In this paper we investigate the distribution of values of L(1,chi) as chi ranges over primitive real characters. In particular we focus on the extent to which this distribution may be approximated by "random Euler products." Our work also establishes a recent conjecture of Montgomery and Vaughan on the frequency of large (or small) values of L(1,chi). 
1 Citations
An analytic function in 3 variables related to the value-distribution of log $L$, and the "Plancherel volume" (Functions in Number Theory and Their Probabilistic Aspects)
Introduction At the conference, the author spoke on his recent article [7] and on related joint work with Kohji Matsumoto [9, 10]. These papers which contain full details have meanwhile been


A Theorem on the Distribution of the Values of L-Functions
Let (d/n) [where d=0, I (mod 4), d=≠u 2 , u integral] be Kronecker's symbol. Define for s > 0 L s = Σ (d/n) n -s .
The Distribution of the Quadratic Class Number
For each positive integer D which exceeds 1 and which satisfies one of the conditions −D ≡ 0, 1(mod 4), let h(−D) denote the number of classes of primitive binary quadratic forms whose discriminant
On the distribution of the values of quadraticL-series in the half-plane σ>1/2
In this paper we consider the distribution in the half-plane σ>1/2 of the values of DirichletL-series formed with quadratic characters.
Ten lectures on the interface between analytic number theory and harmonic analysis
Uniform distribution van der Corput sets Exponential sums I: The methods of Weyl and van der Corput Exponential sums II: Vinogradov's method An introduction to Turan's method Irregularities of
Topics in Multiplicative Number Theory
Three basic principles.- The large sieve.- Arithmetic formulations of the large sieve.- A weighted sieve and its application.- A lower bound of Roth.- Classical mean value theorems.- New mean value
Large character sums
Assuming the Generalized Riemann Hypothesis, the authors study when a character sum over all n infinity and q -> infinity (q is the size of the finite field).
Multiplicative Number Theory
From the contents: Primes in Arithmetic Progression.- Gauss' Sum.- Cyclotomy.- Primes in Arithmetic Progression: The General Modulus.- Primitive Characters.- Dirichlet's Class Number Formula.- The
On the Class-Number of the Corpus P(√−k)