On logarithmic asymptotics for the number of restricted partitions in the exponential caseстатья
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Аннотация: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.