This web page highlights some of the conjectures and open problems concerning L-functions and Random Matrix Theory.

If you would like to print a hard copy of the whole outline, you can download a dvi, postscript or pdf version.

- Distribution of zeros of L-functions
- The GUE hypothesis
- Correlations of zeros
- Neighbor spacing
- Zeros of derivatives
- Horizontal distribution of zeros of zeta prime
- Statistics of the zeros of the derivative of xi
- Relationship between symplectic and odd orthogonal
- The Alternative Hypothesis
- p-adic L-functions
- Zeros and primes
- The distribution of primes
- Gaps between primes
- Primes of a special form
- An exponential sum involving primes
- Mean-values
- The mean-value conjectures
- Shifted mean values
- Multiple Dirichlet series
- Ratios of zeta-functions
- Lower order terms
- Mollified mean values
- Moments of S(T)
- The integral of exp(i lambda S(t))
- High moments are not natural
- Critical values
- Extremal problems
- Critical values
- The maximal order of S(T)
- The maximal order of the zeta-function on the critical line
- The maximal rank of an elliptic curve as a function of its conductor
- The distribution of Fourier coefficients of half-integral weight forms
- Omega results for twists
- Non-critical values
- Difficult to classify
- Function field zeta-functions
- Fixed q
- Corrections for small degree
- Effective computation of zeta-functions
- More function field analogues
- Distribution of sha
- Random matrix questions
- Derivatives of characteristic polynomials
- Eigenvalues of high powers of a matrix
- p-adic random matrix theory
- Miscellaneous topics

The individual contributions may have problems because converting complicated TeX into a web page is not an exact science. The dvi, ps, or pdf versions are your best bet.