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On logarithmic
asymptotics for the number of restricted partitions in the
exponential case
Murat V. Vakhitov and Dmitrii S. Minenkov |
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Vol. 12 (2023), No. 4, 297–309
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DOI: 10.2140/moscow.2023.12.297
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Abstract |
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Asymptotics for the logarithm of the number of restricted partitions is calculated in the case of exponential growth of the counting function. In terms of abstract number theory this problem is the inverse problem of the distribution of abstract primes, i.e., for a given counting function of abstract primes we calculate the asymptotics of abstract integers. While calculating the number of integers, only the limited number of abstract primes is considered and the constructed asymptotics is uniform with respect to this number. We consider only the leading term of logarithmic asymptotics, which is obtained using elementary estimations. The considered case includes the case of integers and primes themselves. |
Keywords
restricted partitions, abstract primes, abstract integers,
counting function, asymptotics
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Mathematical Subject Classification
Primary: 11P70, 11P81
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Milestones
Received: 27 May 2022
Revised: 25 November 2023
Accepted: 12 December 2023
Published: 5 January 2024
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Authors |
| Murat V. Vakhitov | |
| Department of Mechanics and
Mathematics Lomonosov Moscow State University Moscow Russia |
National Research University Higher
School of Economics Moscow Russia |
| Dmitrii S. Minenkov | |
| Ishlinsky Institute for Problems in
Mechanics Moscow Russia |
National Research University Higher
School of Economics Moscow Russia |
| © 2023 MSP (Mathematical Sciences Publishers). |
