Geodesic
On the Asymptotics of the Element Counting Function in an Additive Arithmetic Semigroup with Exponential Counting Function of Prime Generators
Funkcionalʹnyj analiz i ego priloženiâ, Tome 50 (2016) no. 4, pp. 55-75

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We find the asymptotics of the element counting function for an additive arithmetic semigroup with exponential growth of the counting function of prime generators.
Keywords: arithmetic semigroup, inverse abstract prime number theorem, counting function, entropy, asymptotics. 
@article{FAA_2016_50_4_a5,
     author = {D. S. Minenkov and V. E. Nazaikinskii and V. L. Chernyshev},
     title = {On the {Asymptotics} of the {Element} {Counting} {Function} in an {Additive} {Arithmetic} {Semigroup} with {Exponential} {Counting} {Function} of {Prime} {Generators}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {55--75},
     publisher = {mathdoc},
     volume = {50},
     number = {4},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2016_50_4_a5/}
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D. S. Minenkov; V. E. Nazaikinskii; V. L. Chernyshev. On the Asymptotics of the Element Counting Function in an Additive Arithmetic Semigroup with Exponential Counting Function of Prime Generators. Funkcionalʹnyj analiz i ego priloženiâ, Tome 50 (2016) no. 4, pp. 55-75. http://geodesic.mathdoc.fr/item/FAA_2016_50_4_a5/