| Title |
Remarks on the connection of the Riemann hypothesis to self-approximation / |
| Authors |
Laurinčikas, Antanas |
| DOI |
10.3390/computation12080164 |
| Full Text |
|
| Is Part of |
Computation.. Basel : MDPI. 2024, vol. 12, iss. 8, art. no. 164, p. [1-7].. eISSN 2079-3197 |
| Keywords [eng] |
Riemann hypothesis ; Riemann zeta-function ; universality ; weak convergence |
| Abstract [eng] |
By the Bagchi theorem, the Riemann hypothesis (all non-trivial zeros lie on the critical line) is equivalent to the self-approximation of the function (Formula presented.) by shifts (Formula presented.). In this paper, it is determined that the Riemann hypothesis is equivalent to the positivity of density of the set of the above shifts approximating (Formula presented.) with all but at most countably many accuracies (Formula presented.). Also, the analogue of an equivalent in terms of positive density in short intervals is discussed. |
| Published |
Basel : MDPI |
| Type |
Journal article |
| Language |
English |
| Publication date |
2024 |
| CC license |
|
