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Negative energy, debts, and disinformation from the viewpoint of analytic number theory. (English) Zbl 1362.82023
Summary: The number zero and negative numbers are added to analytical number theory which includes transcendents. New solutions of Diophantine equations are applied to thermodynamics, information theory and biology.
MSC:
82B30 Statistical thermodynamics
11D04 Linear Diophantine equations
94A24 Coding theorems (Shannon theory)
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[1] L. D. Landau and E. M. Lifshits, Statistical Physics (Nauka, Moscow, 1964) [in Russian]. · Zbl 0859.76001
[2] Maslov, V.P.; Nazaikinskii, V.E., On the rate of convergence to the Bose-Einstein distribution, Math. Notes, 99, 95-109, (2016) · Zbl 1338.82051
[3] Vershik, A. M., Statistical mechanics of combinatorial partitions, and their limit shapes, Funktsional. Anal. i Prilozhen., 30, 19-39, (1996) · Zbl 0868.05004
[4] Maslov, V. P.; Nazaikinskii, V. E., Disinformation theory for bosonic computational media, Math. Notes, 99, 895-900, (2016) · Zbl 1349.82022
[5] Weyl, H., Über die asymptotische verteilung der eigenwerte, 110-117, (1911) · JFM 42.0432.03
[6] Courant, R., Über die eigenwerte bei den differentialgleichungen der mathematischen physik, Math. Z., 7, 1-57, (1920) · JFM 47.0455.02
[7] Agmon, S., Asymptotic formulas with remainder estimates for eigenvalues of elliptic operators, Arch. Rational Mech. Anal., 28, 165-183, (1968) · Zbl 0159.15903
[8] G. E. Andrews, The Theory of Partitions (Addison-Wesley, Reading, Mass., 1976). · Zbl 0371.10001
[9] Hardy, G. H.; Ramanujan, S., Asymptotic formulae in combinatory analysis, Proc. London Math. Soc., 2, 75-115, (1917) · JFM 46.0198.04
[10] Rademacher, H., On the partition function \(p\)(\(n\)), Proc. London Math. Soc., 2, 241-254, (1937) · Zbl 0017.05503
[11] Erdős, P.; Lehner, J., The distribution of the number of summands in the partitions of A positive integer, Duke Math. J., 8, 335-345, (1941) · Zbl 0025.10703
[12] Vershik, A. M., Limit distribution of the energy of A quantum ideal gas from the viewpoint of the theory of partitions of natural numbers, Uspekhi Mat. Nauk, 52, 139-146, (1997)
[13] Vershik, A. M.; Freiman, G. A.; Yakubovich, Yu. V., A local limit theorem for random strict partitions, Teor. Veroyatnost. Primenen., 44, 506-525, (1999) · Zbl 0969.60034
[14] Maslov, V. P., 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, 870-877, (2005) · Zbl 1112.91036
[15] V. P. Maslov, Quantum Economics (Nauka, Moscow, 2005) [in Russian]. · Zbl 1182.91134
[16] Maslov, V. P.; Nazaikinskii, V. E., On the distribution of integer random variables related by A certain linear inequality, I, Mat. Zametki, 83, 232-263, (2008) · Zbl 1150.82017
[17] Maslov, V. P.; Nazaikinskii, V. E., On the distribution of integer random variables related by A certain linear inequality, II, Mat. Zametki, 83, 381-401, (2008) · Zbl 1153.82001
[18] Maslov, V. P.; Nazaikinskii, V. E., On the distribution of integer random variables related by A certain linear inequality, III, Mat. Zametki, 83, 880-898, (2008) · Zbl 1202.82006
[19] A. G. Postnikov, Introduction to Analytic Number Theory (Nauka, Moscow, 1971). · Zbl 0231.10001
[20] J. Knopfmacher, Abstract Analytic Number Theory (North-Holland, Amsterdam, 1975). · Zbl 0322.10001
[21] A. A. Karatsuba Fundamentals of Analytic Number Theory (URSS, Moscow, 2004) [in Russian].
[22] Bredikhin, B. M., Elementary solution of inverse problems on bases of free semigroups, Mat. Sb., 50, 221-232, (1960)
[23] Maslov, V. P., Mathematical justification for the transition to negative pressures of the new ideal liquid, Math. Notes, 92, 402-411, (2012) · Zbl 1469.76004
[24] Maslov, V. P., Case of less than two degrees of freedom, negative pressure, and the Fermi-Dirac distribution for a hard liquid, Math. Notes, 98, 138-157, (2015) · Zbl 1329.82128
[25] Nazaikinskii, V. E., On the asymptotics of the number of states for the Bose-Maslov gas, Math. Notes, 91, 816-823, (2012) · Zbl 1285.82048
[26] A. N. Kolmogorov, Jubilee Collection of Works in Three Volumes Ed. by A. N. Shiryaev (Fizmatlit, Moscow, 2003).
[27] Maslov, V. P., New thermodynamics and frost cleft in conifers, Math. Notes, 98, 343-347, (2015)
[28] Maslov, V. P.; Maslov, A. V., On the spectral gap in the region of negative pressures, Math. Notes, 99, 711-714, (2016) · Zbl 1351.82100
[29] V. N. Kolokoltsov and V. P. Maslov, Idempotent Analysis and Its Applications (Kluwer Academic Publ., Dordrecht /Boston/London, 1997). · Zbl 0941.93001
[30] Maslov, V. P., Mathematical conception of “phenomenological” equilibrium thermodynamics, Russ. J. Math. Phys., 18, 363-370, (2011) · Zbl 1326.82009
[31] Maslov, V. P., New construction of classical thermodynamics and UD-statistics, Russian J. Math. Phys., 21, 256-284, (2014) · Zbl 1311.82019
[32] A. I. Burshtein, Molecular Physics (Nauka, Novosibirsk, 1986) [in Russian].
[33] Perron, O., Zur theorie der dirichletschen reihen, J. für die reine und angewandte Mathematik, 134, 95-143, (1908) · JFM 39.0328.02
[34] G. H. Hardy and M. Riesz, The General Theory of Dirichlet’s Series (Cambridge University Press, Cambridge, 1915). · JFM 45.0387.03
[35] Minenkov, D. S.; Nazaikinskii, V. E.; Chernyshev, V. L., On the Bose-Maslov statistics in the case of infinitely many degrees of freedom, Dokl. Ross. Akad. Nauk, 468, 618-621, (2016) · Zbl 1357.11095
[36] Minenkov, D. S.; Nazaikinskii, V. E.; Chernyshev, V. L., On the asymptotics of the counting function of elements in an additive arithmetic semigroup with exponential counting function of prime generators, (2016) · Zbl 1366.11105
[37] M. V. Fedoryuk, The Saddle-Point Method (Nauka, Moscow, 1977) [in Russian]. · Zbl 0463.41020
[38] Maslov, V. P.; Nazaikinskii, V. E., On the distribution of integer random variables satisfying two linear relations, Mat. Zametki, 84, 69-98, (2008) · Zbl 1219.60031
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