Arithmetic properties of values of divergent in C series. Conjectures
https://doi.org/10.22405/2226-8383-2025-26-3-300-306
Abstract
The article describes the directions of research on the arithmetic properties of series values of the form
with coefficients 𝑎𝑛 satisfying certain conditions. Under these conditions, the considered series, other than the polynomial, converges in the field C only at 𝑧 = 0. However, for almost all but a finite number of primes, such a series converges in the fields Q𝑝. Therefore there are two ways of research. We can either consider the arithmetic properties of the result of some summation of this series, or consider the values of this series in the field Q𝑝. The paper formulates conjectures, related to the values of the considered series.
About the Author
Vladimir Grigorevich Chirskii
Lomonosov Moscow State University; Russian Presidential Academy of National Economy and Public Administration
Russian Federation
Russian Federation
doctor of physical and mathematical sciences
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Review
For citations:
Chirskii V.G. Arithmetic properties of values of divergent in C series. Conjectures. Chebyshevskii Sbornik. 2025;26(3):300-306. (In Russ.) https://doi.org/10.22405/2226-8383-2025-26-3-300-306
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