TY  - JOUR
A1  - Steuding, Jörn
A1  - Tongsomporn, Janyarak
T1  - On the order of growth of Lerch zeta functions
JF  - Mathematics
N2  - We extend Bourgain’s bound for the order of growth of the Riemann zeta function on the critical line to Lerch zeta functions. More precisely, we prove L(λ, α, 1/2 + it) ≪ t\(^{13/84+ϵ}\) as t → ∞. For both, the Riemann zeta function as well as for the more general Lerch zeta function, it is conjectured that the right-hand side can be replaced by t\(^ϵ\) (which is the so-called Lindelöf hypothesis). The growth of an analytic function is closely related to the distribution of its zeros.
KW  - Lerch zeta function
KW  - Hurwitz zeta function
KW  - (approximate) functional equation
KW  - order of growth
KW  - exponent pairs
KW  - MSC 11M35
Y1  - 2023
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:20-opus-303981
SN  - 2227-7390
VL  - 11
IS  - 3
ER  -