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References
- Adamchik, V. S. On the Barnes function. Proceedings of the 2001 International Symposium on Symbolic and Algebraic Computation, 15--20 (electronic), ACM, New York, 2001. MR2044587 (2005a:33001)
- Andrews, George E.; Askey, Richard; Roy, Ranjan. Special functions.Encyclopedia of Mathematics and its Applications, 71. Cambridge University Press, Cambridge, 1999. xvi+664 pp. ISBN: 0-521-62321-9; 0-521-78988-5 MR1688958 (2000g:33001)
- Barnes,E.W: The theory of the G-function, Quart. J. Pure Appl. Math. 31 (1899), 264--314.
- Biane, Philippe; Pitman, Jim; Yor, Marc. Probability laws related to the Jacobi theta and Riemann zeta functions, and Brownian excursions. Bull. Amer. Math. Soc. (N.S.) 38 (2001), no. 4, 435--465 (electronic). MR1848256 (2003b:11083)
- Biane, Ph.; Yor, M. Valeurs principales associées aux temps locaux browniens.(French) [Principal values associated with Brownian local times] Bull. Sci. Math. (2) 111 (1987), no. 1, 23--101. MR0886959 (88g:60188)
- Bondesson, Lennart. Generalized gamma convolutions and related classes of distributions and densities.Lecture Notes in Statistics, 76. Springer-Verlag, New York, 1992. viii+173 pp. ISBN: 0-387-97866-6 MR1224674 (94g:60031)
- Bottcher, A. ; Silbermann. B: Analysis of Toeplitz operators, Springer-Verlag, Berlin. Second Edition (2006).
- Bourgade, P.; Hughes, C. P.; Nikeghbali, A.; Yor, M. The characteristic polynomial of a random unitary matrix: a probabilistic approach. Duke Math. J. 145 (2008), no. 1, 45--69. MR2451289 (2009j:60011)
- Carmona, Philippe; Petit, Frédérique; Yor, Marc. On the distribution and asymptotic results for exponential functionals of Lévy processes. Exponential functionals and principal values related to Brownian motion, 73--130, Bibl. Rev. Mat. Iberoamericana, Rev. Mat. Iberoamericana, Madrid, 1997. MR1648657 (99h:60144)
- Chaumont, L.; Yor, M. Exercises in probability.A guided tour from measure theory to random processes, via conditioning.Cambridge Series in Statistical and Probabilistic Mathematics, 13. Cambridge University Press, Cambridge, 2003. xvi+236 pp. ISBN: 0-521-82585-7 MR2016344 (2004m:60001)
- Fuchs, A.; Letta, G. Un résultat élémentaire de fiabilité. Application à la formule de Weierstrass sur la fonction gamma.(French) [An elementary reliability result. Application to the Weierstrass formula on the gamma function] Séminaire de Probabilités, XXV, 316--323, Lecture Notes in Math., 1485, Springer, Berlin, 1991. MR1187789 (93k:60034)
- Gordon, Louis. A stochastic approach to the gamma function. Amer. Math. Monthly 101 (1994), no. 9, 858--865. MR1300491 (95k:33003)
- Jacod. J, Kowalski. E and Nikeghbali. A: Mod-Gaussian convergence: new limit theorems in probability and number theory, http://arxiv.org/pdf/0807.4739 (2008).
- James, Lancelot F.; Roynette, Bernard; Yor, Marc. Generalized gamma convolutions, Dirichlet means, Thorin measures, with explicit examples. Probab. Surv. 5 (2008), 346--415. MR2476736
- Keating, J. P. $L$-functions and the characteristic polynomials of random matrices. Recent perspectives in random matrix theory and number theory, 251--277, London Math. Soc. Lecture Note Ser., 322, Cambridge Univ. Press, Cambridge, 2005. MR2166465 (2006m:11126)
- Keating, J. P.; Snaith, N. C. Random matrix theory and $zeta(1/2+it)$. Comm. Math. Phys. 214 (2000), no. 1, 57--89. MR1794265 (2002c:11107)
- Lebedev, N. N. Special functions and their applications.Revised edition, translated from the Russian and edited by Richard A. Silverman.Unabridged and corrected republication.Dover Publications, Inc., New York, 1972. xii+308 pp. MR0350075 (50 #2568)
- Recent perspectives in random matrix theory and number theory.Edited by F. Mezzadri and N. C. Snaith.London Mathematical Society Lecture Note Series, 322. Cambridge University Press, Cambridge, 2005. x+518 pp. ISBN: 978-0-521-62058-1; 0-521-62058-9 MR2145172 (2006c:11002)
- Revuz, Daniel; Yor, Marc. Continuous martingales and Brownian motion.Third edition.Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 293. Springer-Verlag, Berlin, 1999. xiv+602 pp. ISBN: 3-540-64325-7 MR1725357 (2000h:60050)
- Sato. K: LÃvy processes and infinitely divisible distributions}, Cambridge University Press 68, (1999).
- Thorin, Olof. On the infinite divisibility of the lognormal distribution. Scand. Actuar. J. 1977, no. 3, 121--148. MR0552135 (80m:60022)
- Voros, A. Spectral functions, special functions and the Selberg zeta function. Comm. Math. Phys. 110 (1987), no. 3, 439--465. MR0891947 (89b:58173)

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