| Title |
On equivalents of the Riemann hypothesis connected to the approximation properties of the zeta function |
| Authors |
LaurinΔikas, Antanas |
| DOI |
10.3390/axioms14030169 |
| Full Text |
|
| Is Part of |
Axioms.. Basel : MDPI. 2025, vol. 14, iss. 3, art. no. 169, p. [1-13].. eISSN 2075-1680 |
| Keywords [eng] |
Gram function ; Riemann hypothesis ; Riemann zeta function ; limit theorem ; universality ; weak convergence of probability measures |
| Abstract [eng] |
The famous Riemann hypothesis (RH) asserts that all non-trivial zeros of the Riemann zeta function π(π ) (zeros different from π =β2π , πββ ) lie on the critical line π=1/2 . In this paper, combining the universality property of π(π ) with probabilistic limit theorems, we prove that the RH is equivalent to the positivity of the density of the set of shifts π(π +ππ‘π) approximating the function π(π ) . Here, π‘π denotes the Gram function, which is a continuous extension of the Gram points. |
| Published |
Basel : MDPI |
| Type |
Journal article |
| Language |
English |
| Publication date |
2025 |
| CC license |
|
