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The method

Moments of zeta and correlations of divisor-sums, I (second moment of zeta) Conrey, J. B. and Keating, J. P., doi-journal
Moments of zeta and correlations of divisor-sums, II (fourth moment of zeta) Conrey, J. B. and Keating, J. P., doi-journal
Moments of zeta and correlations of divisor-sums, III ($2k$th moment, one swap) Conrey, J. B. and Keating, J. P., doi-journal
Moments of zeta and correlations of divisor-sums, IV ($2k$th moment, two swaps) Conrey, J. B. and Keating, J. P.
Pair correlation and twin primes revisited Conrey, J. B. and Keating, J. P.

Foundations of the method

Random matrix theory and the Riemann zeros. I. Three-and four-point correlations Bogomolny, E. B. and Keating, J. P., doi-journal
Random matrix theory and the Riemann zeros. II. $n$-point correlations Bogomolny, E. B. and Keating, J. P., doi-journal
High moments of the Riemann zeta-function Conrey, J. B. and Gonek, S. M., doi-journal
A quadratic divisor problem Duke, W., Friedlander, J. B., and Iwaniec, H., doi-journal
Mean value theorems for long Dirichlet polynomials and tails of Dirichlet series Goldston, D. A. and Gonek, S. M., doi-journal

Connections with the circle method

Pairs of diagonal quadratic forms and linear correlations among sums of two squares Browning, T. D. and Munshi, R., doi-journal
The circle method and pairs of quadratic forms Iwaniec, H. and Munshi, R., doi-journal
The circle method and bounds for $L$-functions — I Munshi, R., doi-journal
The circle method and bounds for $L$-functions — {II}: Subconvexity for twists of ${ GL}(3)$ $L$-functions Munshi, R., doi-journal
The circle method and bounds for $L$-functions — {III}: $t$-aspect subconvexity for $GL(3)$ $L$-functions Munshi, R., doi-journal
The circle method and bounds for $L$-functions — {IV}: Subconvexity for twists of $ GL(3)$ $L$-functions Munshi, R., doi-journal
Vinogradov's mean value theorem via efficient congruencing Wooley, T. D., doi-journal
Vinogradov's mean value theorem via efficient congruencing, II Wooley, T. D., doi-journal
The cubic case of the main conjecture in Vinogradov's mean value theorem Wooley, T. D., doi-journal

Applications to convolution sums and divisor sums

Averages of shifted convolutions of $d_3(n)$ Baier, S., Browning, T. D., Marasingha, G., and Zhao, L., doi-journal
Shifted convolution sums and subconvexity bounds for automorphic $L$-functions Blomer, V., doi-journal
An additive divisor problem Deshouillers, J.-M., and Iwaniec, H., doi-journal
On the exponent of distribution of the ternary divisor function Fouvry, E., Kowalski, E., and Michel, P., doi-journal
The divisor function over arithmetic progressions Fouvry, E., and Iwaniec, H., doi-journal
Incomplete Kloosterman sums and a divisor problem Friedlander, J. B. and Iwaniec, H., doi-journal
The additive divisor problem and its analogs for Fourier coefficients of cusp forms. I Jutila, M., doi-journal
On the variance of sums of divisor functions in short intervals Lester, S.
On the distribution of the divisor function and Hecke eigenvalues Lester, S., and Yesha, N.
Multiplicative functions in short intervals Matomäki, K., and Radziwił\l, M., doi-journal
An averaged form of Chowla's conjecture Matomäki, K., Radziwił\l, M., and Tao, T., doi-journal
The subconvexity problem for Rankin-Selberg $L$-functions and equidistribution of Heegner points Michel, P., doi-journal
Mean values of character sums Montgomery, H. L. and Vaughan, R. C., doi-journal
Shifted convolution of divisor function $d_3$ and Ramanujan $\tau$ function Munshi, R.
Shifted convolution sums for $GL(3)\timesGL(2)$ Munshi, R., doi-journal
On shifted convolutions of $\zeta^3(s)$ with automorphic $L$-functions Pitt, N. J. E., doi-journal

Moments of $L$-functions in the number field setting

The shifted fourth moment of automorphic L-functions of prime power level Balkanova, O.
New error term for the fourth moment of automorphic $L$-functions Balkanova, O. and Frolenkov, D.
A uniform asymptotic formula for the second moment of primitive $L$-functions on the critical line Balkanova, O. and Frolenkov, D.
The second moment of the Riemann zeta function with unbounded shifts Bettin, S., doi-journal
The mean square of the product of the Riemann zeta-function with Dirichlet polynomials Bettin, S., Chandee, V., and Radziwił\l, M., doi-journal
A hybrid Euler-Hadamard product and moments of $\zeta'(\rho)$ Bui, H. M., Gonek, S. M., and Milinovich, M. B., doi-journal
The eighth moment of Dirichlet $L$-functions Chandee, V. and Li, X., doi-journal
Integral moments of $L$-functions Conrey, J. B., Farmer, D. W., Keating, J. P., Rubinstein, M. O., and Snaith, N. C., doi-journal
Lower order terms in the full moment conjecture for the Riemann zeta function Conrey, J. B., Farmer, D. W., Keating, J. P., Rubinstein, M. O., and Snaith, N. C., doi-journal
The cubic moment of central values of automorphic $L$-functions Conrey, J. B., and Iwaniec, H., doi-journal
Lower order terms for the moments of symplectic and orthogonal families of $L$-functions Goulden, I. P., Huynh, D. K., and Rishikesh, Rubinstein, M. O., doi-journal
The twisted fourth moment of the Riemann zeta function Hughes, C. P. and Young, M. P., doi-journal
On the mean value of $L({1\over 2},\,\chi )$ for real characters Jutila, M., doi-journal
Upper bounds for moments of $\zeta'(\rho)$ Milinovich, M. B., doi-journal
Moments of products of automorphic $L$-functions Milinovich, M. B., and Turnage-Butterbaugh, C. L., doi-journal
Lower bounds for moments of $\zeta'(\rho)$ Milinovich, M. B., and Ng, N., doi-journal
The fourth moment of $\zeta'(\rho)$ Ng, N., doi-journal
Nonvanishing of quadratic Dirichlet $L$-functions at $s=\frac{1}2$ Soundararajan, K., doi-journal

Moments of $L$-functions and convolution sums in the function field setting

Shifted convolution and the Titchmarsh divisor problem over $\Bbb F_q[t]$ Andrade, J. C., Bary-Soroker, L., and Rudnick, Z., doi-journal
The mean value of $L(\frac12,\chi)$ in the hyperelliptic ensemble Andrade, J. C. and Keating, J. P., doi-journal
Conjectures for the integral moments and ratios of $L$-functions over function fields Andrade, J. C. and Keating, J. P., doi-journal
The second and third moment of $L(1/2,\chi)$ in the hyperelliptic ensemble Florea, A.
Improving the error term in the mean value of $L(1/2,\chi)$ in the hyperelliptic ensemble Florea, A.
Mean values of multiplicative functions over function fields Granville, A., Harper, A., and Soundararajan, K.
Sums of divisor functions in $\mathbb{F}_q[t]$ and matrix integrals Keating, J. P., Rodgers, B., Roditty-Gershon, E., and Rudnick, Z.
Moments of zeta functions associated to hyperelliptic curves over finite fields Rubinstein, M., and Wu, K., doi-journal