References
S. M. Avdoshin, V. V. Belov, and V. P. Maslov, Mathematical Aspects of Design of Computational Media (MIEM, Moscow, 1984) [in Russian].
S. M. Avdoshin, V. V. Belov, V. P. Maslov, and A. M. Chebotarev, Design of Computational Media: Mathematical Aspects, in Mathematical Aspects of Computer Engineering. Advances in Science and Technology in USSR, V. P. Maslov and K. A. Volosov (eds.) (Moscow: Mir, 1988).
V. P. Maslov and A. V. Maslov, “On the spectral gap in the region of negative pressures,” Math. Notes 99 (5–6), 711–714 (2016).
L. D. Landau and I. M. Lifshits, Theoretical Physics, vol. 4: Statistical Physics (GITTL, Moscow–Leningrad, 1951) [in Russian].
H. Weyl, “Über die asymptotische Verteilung der Eigenwerte,” Göttinger Nachr., 110–117 (1911).
R. Courant, “Über die Eigenwerte bei den Differentialgleichungen der mathematischen Physik,” Math. Z. 7, 1–57 (1920).
S. Agmon, “Asymptotic formulas with remainder estimates for eigenvalues of elliptic operators,” Arch. Rational Mech. Anal. 28, 165–183 (1968).
G. E. Andrews, The Theory of Partitions (Addison–Wesley, Reading, Mass., 1976).
G. H. Hardy and S. Ramanujan “Asymptotic formulae in combinatory analysis,” Proc. London Math. Soc. (2) 17, 75–115 (1917).
H. Rademacher, “On the partition function p(n),” Proc. LondonMath. Soc. (2) 43, 241–254 (1937).
P. Erdos and J. Lehner, “The distribution of the number of summands in the partitions of a positive integer,” Duke Math. J. 8, 335–345 (1941).
A.M. Vershik, “Statistical mechanics of combinatorial partitions, and their limit shapes,” Funktsional. Anal. i Prilozhen. 30 (2), 19–39 (1996) [Functional Anal. Appl. 30 (2), 95–105 (1996)].
A. M. Vershik, “Limit distribution of the energy of a quantum ideal gas from the viewpoint of the theory of partitions of natural numbers,” UspekhiMat. Nauk 52 (2), 139–146 (1997) [Russian Math. Surveys 52 (2), 379–386 (1997)].
A. M. Vershik, G. A. Freiman, and Yu. V. Yakubovich, “A local limit theorem for random strict partitions,” Teor. Veroyatnost. Primenen. 44 (3), 506–525 (1999) [Theory Probab. Appl. 44 (3) 453–468 (2000)].
V. P. Maslov, “On a general theorem of set theory leading to the Gibbs, Bose–Einstein, and Pareto distributions as well as to the Zipf–Mandelbrot law for the stock market,” Mat. Zametki 78 (6), 870–877 (2005) [Math. Notes 78 (5–6), 807–813 (2005)].
V. P. Maslov, Quantum Economics (Nauka, Moscow, 2005) [in Russian].
V. P. Maslov and V. E. Nazaikinskii, “On the distribution of integer random variables related by a certain linear inequality, I,” Mat. Zametki 83 (2), 232–263 (2008) [Math. Notes 83 (1–2), 211–237 (2008)].
V. P. Maslov and V. E. Nazaikinskii, “On the distribution of integer random variables related by a certain linear inequality, II,” Mat. Zametki 83 (3), 381–401 (2008) [Math. Notes 83 (3–4), 345–363 (2008)].
V. P. Maslov and V. E. Nazaikinskii, “On the distribution of integer random variables related by a certain linear inequality, III,” Mat. Zametki 83 (6), 880–898 (2008) [Math. Notes 83 (5–6), 804–820 (2008)].
V. P. Maslov and V. E. Nazaikinskii, “On the rate of convergence to the Bose-Einstein distribution,” Math. Notes 99 (1–2), 95–109 (2016).
V. E. Nazaikinskii, “On the asymptotics of the number of states for the Bose–Maslov gas,” Math. Notes 91 (5–6), 816–823 (2012).
P. Billingsley, “On the distribution of large prime divisors,” Periodica Mathematica Hungarica 2, 283–289 (1972).
D. E. Knuth and L. T. Pardo, “Analysis of a simple factorization algorithm,” Theor. Comput. Sci. 3 (1976), 321–348 (1977).
A. M. Vershik, “The asymptotic distribution of factorizations of natural numbers into prime divisors,” Dokl. Akad. Nauk SSSR 289 (2), 269–272 (1986). [SovietMath. Dokl. 34, 57–61 (1987)].
J. Knopfmacher, Abstract Analytic Number Theory (North-Holland, Amsterdam, 1975).
A. A. Karatsuba Fundamentals of Analytic Number Theory (URSS, Moscow, 2004) [in Russian].
D. S. Minenkov, V. E. Nazaikinskii, and V. L. Chernyshev, “On the Bose–Maslov statistics in the case of infinitely many degrees of freedom,” Dokl. Ross. Akad. Nauk 468 (6), 618–621 (2016) [Dokl. Math. 93 (3), 1–3 (2016)].
D. S. Minenkov, V. E. Nazaikinskii, and V. L. Chernyshev, On the asymptotics of the counting function of elements in an additive arithmetic semigroup with exponential counting function of prime generators, Funktsional. Anal. Prilozhen. (to appear in 2016).
V. P. Maslov and V. E. Nazaikinskii, “On the distribution of integer random variables satisfying two linear relations,” Mat. Zametki 84 (1), 69–98 (2008) [Math. Notes 84 (1–2), 73–99 (2008)].
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Maslov, V.P., Nazaikinskii, V.E. Disinformation theory for bosonic computational media. Math Notes 99, 895–900 (2016). https://doi.org/10.1134/S000143461605028X
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DOI: https://doi.org/10.1134/S000143461605028X