| Title |
On the Mishou theorem for zeta-functions with periodic coefficients |
| Authors |
Balčiūnas, Aidas ; Jasas, Mindaugas ; Macaitienė, Renata ; Šiaučiūnas, Darius |
| DOI |
10.3390/math11092042 |
| Full Text |
|
| Is Part of |
Mathematics.. Basel : MDPI. 2023, vol. 11, iss. 9, art. no. 2042, p. ]1-10].. eISSN 2227-7390 |
| Keywords [eng] |
Hurwitz zeta-function ; joint universality ; periodic Hurwitz zeta-function ; periodic zetafunction ; universality |
| Abstract [eng] |
Let a = famg and b = fbmg be two periodic sequences of complex numbers, and, additionally, a is multiplicative. In this paper, the joint approximation of a pair of analytic functions by shifts (znT(s + it; a), znT(s + it, a; b)) of absolutely convergent Dirichlet series znT(s; a) and znT(s, a; b) involving the sequences a and b is considered. Here, nT ! ¥ and nT T2 as T ! ¥. The coefficients of these series tend to am and bm, respectively. It is proved that the set of the above shifts in the interval [0, T] has a positive density. This generalizes and extends the Mishou joint universality theorem for the Riemann and Hurwitz zeta-functions. |
| Published |
Basel : MDPI |
| Type |
Journal article |
| Language |
English |
| Publication date |
2023 |
| CC license |
|
