1. Introduction ................................................. 5
2. Preliminaries ................................................ 7
2.1. Dirichlet characters and Gaussian sums .................. 7
2.2. Dirichlet L-functions .................................. 10
2.3. Estimates for character sums ........................... 11
2.4. Some methods of estimation ............................. 15
3. The mean square of quadratic Dirichlet L-functions at 1 ..... 16
3.1. Sum over even characters with odd modulus;
a preliminary decomposition ............................ 16
3.2. Smoothing and transforming the q-sums .................. 21
3.3. Summing the smoothed sums .............................. 24
3.4. Error terms ............................................ 31
3.4.1. The error from the approximation ................ 31
3.4.2. The error from the smoothing .................... 33
3.5. Main theorem ........................................... 34
4. The mean square of primitive quadratic Dirichlet
L-functions at l ............................................ 37
4.1. Mean value estimate for the Möbius function............. 37
4.2. Restriction to primitive characters .................... 38
4.3. The second main term in the primitive case ............. 39
4.4. The mean square over primitive characters .............. 44
5. An application to algebraic number theory ................... 45
5.1. Algebraic integers and ideal classes ................... 45
5.2. Subrings  n ........................................... 46
6. Concluding remarks .......................................... 47
6.1. The mean square over a short interval .................. 47
6.2. Other moments .......................................... 48
References ..................................................... 49
| 
