Geodesic
Summation of Unordered Arrays
Funkcionalʹnyj analiz i ego priloženiâ, Tome 52 (2018) no. 1, pp. 43-55

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An approach to the summation of unordered number and matrix arrays based on ordering them by absolute value (greedy summation) is proposed. Theorems on products of greedy sums are proved. A relationship between the theory of greedy summation and the theory of generalized Dirichlet series is revealed. The notion of asymptotic Dirichlet series is considered.
Keywords: greedy sum, unordered sum, theorem on multiplications of sums, generalized Dirichlet series, asymptotic Dirichlet series, Riesz means, generic zeta-function. 
@article{FAA_2018_52_1_a3,
     author = {E. V. Shchepin},
     title = {Summation of {Unordered} {Arrays}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {43--55},
     publisher = {mathdoc},
     volume = {52},
     number = {1},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2018_52_1_a3/}
}
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E. V. Shchepin. Summation of Unordered Arrays. Funkcionalʹnyj analiz i ego priloženiâ, Tome 52 (2018) no. 1, pp. 43-55. http://geodesic.mathdoc.fr/item/FAA_2018_52_1_a3/