
## 3. The Recipe

1. #### Problem 3.1.

[C. Hughes] Can one find a version of the recipe using asymmetric approximate functional equations, giving a “robust” version of the calculations? Similarly, can one apply the Conrey-Keating method using two asymmetric Dirichlet polynomials $$\sum_{m\leq X} \frac{\tau_A(m)}{m^s} \ \ \ \ \ \ \mbox{and} \ \ \ \ \ \ \sum_{n\leq Y} \frac{\tau_B(n)}{n^{1-s}}$$ to get the same answer as before, i.e. when $X=Y$?
• #### Problem 3.2.

[N. Ng] Can one prove the fourth moment formula starting from $$\int \prod_{j=1}^4 \left( \sum_{n\leq x_j} \frac{1}{n^{1/2+it}}+\chi(s) \sum_{n\leq t/x_j} \frac{1}{n^{1/2-it}}\right)\,dt \ ?$$

Cite this as: AimPL: Moments of zeta and correlations of divisor sums, available at http://aimpl.org/zetamoments.