M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions with Formulas , Graphs, and Mathematical Tables, pp.258-259, 1972.

G. Ammar, W. Gragg, and L. , Constructing a unitary Hessenberg matrix from spectral data, Numerical Linear Algebra, Digital Signal Processing and Parallel Algorithms NATO Adv. Sci. Inst. Ser. F Comput. Systems Sci, vol.70, pp.385-395, 1988.

R. Arratia, A. D. Barbour, and S. Tavaré, Logarithmic Combinatorial Structures : A Probabilistic Approach, EMS Monographs in Mathematics, vol.1, 2003.
DOI : 10.4171/000

R. Balasubramanian and K. Ramachandra, On the frequency of Titchmarsh's phenomenon for zeta-III, Proc. Indian Acad. Sci, pp.341-351, 1977.

E. L. Basor and Y. Chen, Toeplitz determinants from compatibility conditions, The Ramanujan Journal, vol.13, issue.153, pp.25-40, 2008.

G. B. Arous and A. Guionnet, Large deviations for Wigner's law and Voiculescu's non-commutative entropy, Probab. Theory Related Fields, pp.517-542, 1997.

M. V. Berry, Semiclassical formula for the number variance of the Riemann zeros, Nonlinearity, vol.1, issue.3, pp.399-407, 1988.

M. V. Berry and J. P. Keating, The Riemann zeros and eigenvalue asymptotics, SIAM Rev, pp.236-266, 1999.

P. Biane, La fonction zeta de Riemann et les probabilités, La fonction zeta, pp.165-193, 2003.

P. Biane, J. Pitman, and M. Yor, Probability laws related to the Jacobi theta and Riemann zeta functions, and Brownian excursions, Bulletin of the American Mathematical Society, vol.38, issue.04, pp.435-465, 2001.

E. B. Bogomolny and J. P. Keating, Gutzwiller's Trace Formula and Spectral Statistics: Beyond the Diagonal Approximation, Physical Review Letters, vol.77, issue.8, pp.1472-1475, 1996.

O. Bohigas and M. J. Giannoni, Chaotic motion and random matrix theories, Lec. Notes on Physics, vol.209, pp.1-99, 1984.

A. Borodin and G. Olshanski, Infinite Random Matrices and Ergodic Measures, Communications in Mathematical Physics, vol.223, issue.1, pp.87-123, 2001.

P. Bourgade, Conditional Haar measures on classical compact groups, The Annals of Probability, vol.37, issue.4, pp.1566-1586, 2009.

P. Bourgade, Mesoscopic fluctuations of the zeta zeros, Probability Theory and Related Fields, pp.3-4

P. Bourgade, C. P. Hughes, A. Nikeghbali, and M. Yor, The characteristic polynomial of a random unitary matrix: A probabilistic approach, Duke Mathematical Journal, vol.145, issue.1, pp.45-69, 2008.

P. Bourgade, T. Fujita, and M. Yor, Euler's formulae for $\zeta(2n)$ and products of Cauchy variables, Electronic Communications in Probability, vol.12, issue.0, pp.73-80, 2007.
DOI : 10.1214/ECP.v12-1244

P. Bourgade, A. Nikeghbali, and A. Rouault, Ewens Measures on Compact Groups and Hypergeometric Kernels, Lecture Notes in Mathematics, pp.351-377, 2006.

P. Bourgade, A. Nikeghbali, and A. Rouault, The characteristic polynomial on compact groups with Haar measure: some equalities in law, Comptes Rendus Mathematique, vol.345, issue.4, pp.229-232, 2007.

P. Bourgade, A. Nikeghbali, and A. Rouault, Circular Jacobi Ensembles and Deformed Verblunsky Coefficients, International Mathematics Research Notices, pp.4357-4394, 2009.

E. Brézin and S. Hikami, Characteristic Polynomials of Random Matrices, Communications in Mathematical Physics, vol.214, issue.1, pp.111-135, 2000.

D. Bump, Lie groups, 2004.

M. J. Cantero, L. Moral, and L. Vel´azquez, Five-diagonal matrices and zeros of orthogonal polynomials on the unit circle, Linear Algebra and its Applications, vol.362, pp.29-56, 2003.

L. Chaumont and M. Yor, Exercises in probability. A guided tour from measure theory to random processes, via conditioning, 2003.

J. B. Conrey, More than 2/5 of zeros of the Riemann zeta function are on the critical line, J. Reine. Angew. Math, vol.399, pp.1-26, 1989.

J. B. Conrey and A. Gamburd, Pseudomoments of the Riemann zeta-function and pseudomagic squares, Journal of Number Theory, vol.117, issue.2, pp.263-278, 2006.

J. B. Conrey and A. Ghosh, On mean values of the zeta function, iii, Proceedings of the Amalfi Conference in Analytic Number Theory, 1992.

J. B. Conrey and S. M. Gonek, High moments of the Riemann zeta function, Duke Math, J, vol.107, pp.577-604, 2001.

J. B. Conrey, D. W. Farmer, J. P. Keating, M. O. Rubinstein, and N. C. Snaith, Integral moments of L-functions, Proceedings of the London Mathematical Society, vol.91, issue.01, pp.33-104, 2005.

M. Coram and P. Diaconis, New tests of the correspondence between unitary eigenvalues and the zeros of Riemann??s zeta function, Journal of Physics A: Mathematical and General, vol.36, issue.12, pp.2883-2906

O. Costin and J. Lebowitz, Gaussian Fluctuation in Random Matrices, Physical Review Letters, vol.75, issue.1, pp.69-72, 1995.

H. Cramer, Uber eine Eigenschaft der normalen Verteilungsfunction, Math. Z, vol.2, issue.41, pp.405-414, 1936.

P. O. Dehaye, Joint moments of derivatives of characteristic polynomials, Algebra & Number Theory, vol.2, issue.1, pp.31-68, 2008.

P. A. Deift and X. Zhou, Steepest Descent Method for Riemann-Hilbert Problem, Ann. Math, pp.295-368, 1993.

P. Diaconis and M. Shahshahani, The Subgroup Algorithm for Generating Uniform Random Variables, Probability in the Engineering and Informational Sciences, vol.1, issue.01, pp.15-32, 1987.
DOI : 10.2307/2045709

P. Diaconis and M. Shahshahani, On the eigenvalues of random matrices, Studies in applied probability, J. Appl. Probab, pp.31-49, 1994.

A. Diaconu, D. Goldfeld, and J. Hoffstein, Multiple Dirichlet Series and Moments of Zeta and L-Functions, Compositio Mathematica, vol.139, issue.3, pp.297-360, 2003.

I. Dumitriu and A. Edelman, Matrix models for beta ensembles, Journal of Mathematical Physics, vol.43, issue.11, pp.5830-5847, 2002.
DOI : 10.1063/1.1507823

T. Ehrhardt, A status report on the asymptotic behavior of Toeplitz determinants with Fisher-Hartwig singularities, Oper. Theory Adv, Appl, vol.124, pp.217-241, 2001.

D. W. Farmer, S. M. Gonek, and C. P. Hughes, The maximum size of L-functions, Journal f??r die reine und angewandte Mathematik (Crelles Journal), vol.2007, issue.609, pp.609-215, 2007.

P. J. Forrester, Log-gases and random matrices, book in preparation

P. J. Forrester and N. E. , Applications and generalizations of Fisher???Hartwig asymptotics, Journal of Mathematical Physics, vol.45, issue.5, 2003.
DOI : 10.1063/1.1699484

P. J. Forrester and S. O. Warnaar, The importance of the Selberg integral, Bulletin of the American Mathematical Society, vol.45, issue.4, pp.489-534, 2008.

P. J. Forrester and E. M. Rains, Jacobians and rank 1 perturbations relating to unitary Hessenberg matrices, International Mathematics Research Notices, pp.1-36, 2006.

P. J. Forrester and N. S. Witte, Abstract, Nagoya Mathematical Journal, vol.326, pp.29-114, 2004.

P. J. Forrester and N. S. Witte, Gap probabilities in the finite and scaled Cauchy random matrix ensembles, Nonl, vol.13, pp.1965-1986, 2000.

A. Fujii, Gram's law for the zeta zeros and the eigenvalues of Gaussian unitary ensembles, Proc. Japan Acad. 63 Ser. A, pp.392-395, 1987.
DOI : 10.3792/pjaa.63.392

A. Fujii, Explicit Formulas and Oscillations, Emerging Applications of Number Theory, 1999.

M. Gaudin, Sur la loi limite de l'espacement des valeurs propres d'une matrice ale??atoire, Nuclear Physics, vol.25, pp.447-458, 1961.

M. Gaudin and M. Mehta, On the density of eigenvalues of a random matrix, Nucl. Phys, pp.420-427, 1960.

Y. L. Geronimus, On polynomials orthogonal on the circle, on trigonometric moment problem, and on allied Carath´eodory and Schur functions, Mat. Sb, vol.15, pp.99-130, 1944.

D. A. Goldston, Notes on pair correlation of zeros and prime numbers, in Recent Perspectives in Random Matrix Theory and Number Theory, Note Series, vol.322, 2005.

D. A. Goldston and H. L. Montgomery, Pair correlation of zeros and primes in short intervals, Analytic Number Theory and Diophantine Problems, pp.183-203, 1987.

S. M. Gonek, C. P. Hughes, and J. P. Keating, A hybrid Euler-Hadamard product formula for the Riemann zeta function, Duke Math, J, vol.136, issue.3, pp.507-549, 2007.

W. B. Gragg, Positive definite Toeplitz matrices, the Arnoldi process for isometric operators, and Gaussian quadrature on the unit circle 183-198 ; Russian original in " Numerical methods of linear algebra, J. Comput. Appl. Math, vol.46, pp.16-32, 1982.

B. Hambly, P. Keevash, N. O. Connell, and D. Stark, The characteristic polynomial of a random permutation matrix, Stochastic Process, Appl, vol.90, pp.335-346, 2000.

G. H. Hardy and J. E. Littlewood, Contributions to the theory of the Riemann zetafunction and the theory of the distributions of primes, 1918.

D. R. Heath-brown, Fractional Moments of the Riemann Zeta-Function, Journal of the London Mathematical Society, vol.2, issue.1, pp.65-78, 1981.

F. Hiai and D. Petz, A large deviation theorem for the empirical eigenvalue distribution of random unitary matrices, Annales de l'Institut Henri Poincare (B) Probability and Statistics, vol.36, issue.1, pp.71-85, 2000.

F. Hiai and D. Petz, Large deviations for functions of two random projection matrices, Acta Sci. Math. (Szeged), vol.72, pp.581-609, 2006.

L. K. Hua, Harmonic analysis of functions of several complex variables in the classical domains, Transl. Math. Monographs, vol.6, 1958.

C. P. Hughes, J. P. Keating, and N. O. Connell, On the Characteristic Polynomial?? of a Random Unitary Matrix, Communications in Mathematical Physics, vol.220, issue.2, pp.429-451, 2001.

C. P. Hughes, A. Nikeghbali, and M. Yor, An arithmetic model for the total disorder process, Probability Theory and Related Fields, vol.46, issue.1-2, pp.47-59, 2008.

K. Johansson, On fluctuations of eigenvalues of random Hermitian matrices, Duke Math, Journ, vol.91, pp.151-204, 1998.

K. Johansson, On Random Matrices from the Compact Classical Groups, The Annals of Mathematics, vol.145, issue.3, pp.519-545, 1997.
DOI : 10.2307/2951843

K. Johansson, Random matrices and determinantal processes, math-ph, 2005.

W. D. Joyner, Distribution theorems of L-functions, 1986.

N. M. Katz and P. Sarnak, Random Matrices, Frobenius Eigenvalues and monodromy, 1999.
DOI : 10.1090/coll/045

N. M. Katz and P. Sarnak, Zeros of zeta functions and symmetry, Bull, Amer. Soc, vol.36, issue.45, pp.1-26, 1999.

J. P. Keating and N. C. Snaith, Random Matrix Theory and L-Functions at s = 1/2, Communications in Mathematical Physics, vol.214, issue.1, pp.91-110, 2000.

S. V. Khrushchev, Schur's Algorithm, Orthogonal Polynomials, and Convergence of Wall's Continued Fractions in L2(T), Journal of Approximation Theory, vol.108, issue.2, pp.161-248, 2001.

S. V. Khrushchev, Classification Theorems for General Orthogonal Polynomials on the Unit Circle, Journal of Approximation Theory, vol.116, issue.2, pp.268-342, 2002.

R. Killip and M. Stoiciu, Eigenvalue statistics for CMV matrices : from Poisson to clock via C?E, preprint, 2006.

T. Kotnik, Computational estimation of the order of ?(1/2 + it, Math. Comp, pp.949-956, 2004.

A. B. Kuijlaars and M. Vanlessen, Universality for eigenvalue correlations from the modified Jacobi unitary ensemble, International Mathematics Research Notices, pp.1575-1600, 2002.

A. Laurincikas, Limit Theorems for the Riemann Zeta-Function, series : Mathematics and Its Applications, 1996.

J. F. Le and . Gall, Spatial Branching Processes, Random Snakes and Partial Differential Equations, Lectures in Mathematics, 1999.

E. Levin and D. Lubinsky, Universality Limits Involving Orthogonal Polynomials on the Unit Circle, Computational Methods and Function Theory, pp.543-561, 2007.

D. Lubinsky, A new approach to universality limits at the edge of the spectrum, Contemporary Mathematics, pp.458-281, 2008.

D. Lubinsky, A new approach to universality limits involving orthogonal polynomials, Annals of Mathematics, vol.170, issue.2

A. Martínez-finkelshtein, K. T. Mclaughlin, and E. B. Saff, Asymptotics of orthogonal polynomials with respect to an analytic weight with algebraic singularities on the circle, International Mathematics Research Notices, 2006.

M. L. Mehta and J. Cloiseaux, The probabilities for several consecutive eigenvalues of a random matrix, Indian J. Pure Appl. Math, vol.3, pp.329-351, 1972.

M. L. Mehta, Random matrices, Pure and Applied Mathematics Series, vol.142, 2004.

F. Mezzadri, How to Generate Random Matrices from the Classical Compact Groups, Notices of the Amer, Math. Soc, vol.54, pp.592-604, 2007.

F. Mezzadri and N. C. Snaith, Recent Perspectives in Random Matrix Theory and Number Theory, Lecture Note Series 322 (CUP), 2005.

S. J. Miller, -Functions, Experimental Mathematics, vol.15, issue.3, pp.257-279, 2006.

H. L. Montgomery, The pair correlation of zeros of the zeta function, Analytic number theory (Proceedings of Symposium in Pure Mathemathics, pp.181-193, 1972.

H. L. Montgomery, Extreme values of the Riemann zeta function, Commentarii Mathematici Helvetici, vol.52, issue.1, pp.511-518, 1977.
DOI : 10.1007/BF02567383

H. L. Montgomery and R. C. Vaughan, Hilbert's Inequality, Journal of the London Mathematical Society, vol.2, issue.1, pp.73-82, 1974.

Y. A. Neretin, Hua type integrals over unitary groups and over projective limits of unitary groups, Duke Math, J, vol.114, pp.239-266, 2002.

A. M. Odlyzko, The 10 20 th zero of the Riemann zeta function and 70 million of its neighbors, ATT Bell laboratories preprint, 1989.

A. M. Odlyzko, On the distribution of spacings between zeros of the zeta function, Mathematics of Computation, vol.48, issue.177, pp.273-308, 1987.

G. Olshanski, The problem of harmonic analysis on the infinite-dimensional unitary group, Journal of Functional Analysis, vol.205, issue.2, pp.464-524, 2003.

D. Perrin, Géométrie algébrique : une introduction, EDP Sciences Editions, 1995.

V. V. Petrov, Limit Theorems of Probability Theory, 1995.

V. V. Petrov, On a Relation Between an Estimate of the Remainder in the Central Limit Theorem and the Law of the Iterated Logarithm, Theory of Probability & Its Applications, vol.11, issue.3, pp.454-458, 1966.
DOI : 10.1137/1111046

V. V. Petrov, On the Law of the Iterated Logarithm for a Sequence of Independent Random Variables, Theory of Probability & Its Applications, vol.46, issue.3, pp.542-544, 1999.

]. D. Pickrell, Measures on infinite dimensional Grassmann manifolds, Journal of Functional Analysis, vol.70, issue.2, pp.323-356, 1987.

J. Pitman, Combinatorial stochastic processes, Saint-Flour, Lecture Notes in Math, vol.1875, 2002.

E. M. Rains, High powers of random elements of compact Lie groups, Probability Theorey and Related Fields, 1997.

K. Ramachandra, Some remarks on the mean value of the Riemann zetafunction and other Dirichlet series, II, Hardy-Ramanujan, J, vol.3, pp.1-25, 1980.

S. I. Resnick and R. J. Tomkins, Almost sure stability of maxima, Journal of Applied Probability, vol.7, issue.02, pp.387-401, 1973.
DOI : 10.2307/1426000

E. Royer, Fonction ? et matrices aléatoires Physics and Number Theory, IRMA Lectures in Mathematics and Theoretical Physics Eur. Math. Soc, vol.10, pp.165-224, 2006.

Z. Rudnick and P. Sarnak, Zeros of principal L-functions and random matrix theory, Duke Math, J, vol.81, issue.2, pp.269-322, 1996.

A. Selberg, Contributions to the theory of the Riemann zeta-function, Arkiv for, Mathematik og Naturvidenskab B, vol.48, issue.5, pp.89-155, 1946.

A. Selberg, Old and new conjectures and results about a class of Dirichlet series, Proceedings of the Amalfi Conference on Analytic Number Theory (Maiori, pp.367-385, 1989.

B. Simon, Orthogonal Polynomials on the Unit Circle, Part 1 : Classical Theory, 2005.

B. Simon, Orthogonal Polynomials on the Unit Circle, Part 2 : Spectral Theory, 2005.

B. Simon, CMV matrices: Five years after, Journal of Computational and Applied Mathematics, vol.208, issue.1, pp.120-154, 2007.

B. Simon, The Christoffel-Darboux kernel, to appear in " Perspectives in PDE, Harmonic Analysis and Applications " in honor of V.G. Maz'ya's 70th birthday, Proceedings of Symposia in Pure Mathematics

H. Stahl and V. Totik, General Orthogonal Polynomials, in " Encyclopedia of Mathematics and its Applications, 1992.

N. C. Snaith, Derivatives of random matrix characteristic polynomials with applications to elliptic curves, Journal of Physics A: Mathematical and General, vol.38, issue.48, pp.10345-10360, 2005.

N. C. Snaith, The derivative of SO(2N+1) characteristic polynomials and rank 3 elliptic curves, in Ranks of Elliptic Curves and Random Matrix Theory, LMS lecture note series 341, pp.93-107, 2007.

A. Soshnikov, Determinantal random point fields, Russian Mathematical Surveys, vol.55, issue.5, pp.923-975, 2000.

K. Soundararajan, Extreme values of zeta and L-functions, Mathematische Annalen, vol.152, issue.2, pp.467-486, 2008.

K. Soundararajan, Moments of the Riemann zeta-function, to appear in Ann

A. V. Teplyaev, The pure point spectrum of random orthogonal polynomials on the circle, Soviet Math. Dokl. Russian original in Dokl. Akad. Nauk SSSR, vol.44, issue.320, pp.407-411, 1991.

E. C. Titchmarsh, The Theory of the Riemann Zeta Function, 1951.

K. Tsang, The distribution of the values of the zeta function, 1984.

A. Weil, L'intégration dans les groupes topologiques et ses applications, Actualités Scientifiques et Industrielles, 1940.

A. Weil, On the Riemann Hypothesis in Function-Fields, Proceedings of the National Academy of Sciences, vol.27, issue.7, pp.345-349, 1941.

H. Widom, Toeplitz determinants with singular generating functions, Amer, J. Math, pp.95-333, 1973.

K. L. Wieand, Eigenvalue distributions of random matrices in the permutation group and compact Lie groups, 1998.

D. Williams, Brownian motion and the Riemann zeta-function, Disorder in physical systems, pp.361-372, 1990.

M. Yor, A further note on Selberg's integrals, inspired by N. Snaith's results about the distribution of some characteristic polynomials, RIMS Kokyuroku, 2008.