The eighth moment of Dirichlet L -functions

The Fourth Moment of Dirichlet L-functions

Here ∑∗ denotes summation over primitive characters χ (mod q), φ(q) denotes the number of primitive characters (mod q), and ω(q) denotes the number of distinct prime factors of q. Note that φ(q) is a multiplicative function given by φ(p) = p − 2 for primes p, and φ(p) = p(1 − 1/p) for k ≥ 2 (see Lemma 1 below). Also note that when q ≡ 2 (mod 4) there are no primitive characters (mod q), and so ...

The Fourth Moment of Dirichlet L-functions

for certain explicitly computable constants ai. The difficult part of extending Ingham’s result to include the lower-order terms is asymptotically evaluating the off-diagonal terms. The family of all primitive Dirichlet L-functions of modulus q is similar in some ways to the Riemann zeta function in t-aspect, but is more difficult to analyze. In 1981, Heath-Brown obtained an asymptotic formula ...

The Second Moment of Dirichlet Twists of Hecke L-functions

The First Moment of Quadratic Dirichlet L-functions

We obtain an asymptotic formula for the smoothly weighted first moment of primitive quadratic Dirichlet L-functions at the central point, with an error term that is “square-root” of the main term. Our approach uses a recursive technique that feeds the result back into itself, successively improving the error term.

The Sixth Power Moment of Dirichlet L-functions

Understanding moments of families of L-functions has long been an important subject with many number theoretic applications. Quite often, the application is to bound the error term in an asymptotic expression of the average of an arithmetic function. Also, a good bound for a moments can be used to obtain a point-wise bound for an individual L-function in the family; strong enough bounds of this...