@article{SteudingTongsomporn2023,
  author    = {Steuding, J{\"o}rn and Tongsomporn, Janyarak},
  title     = {On the order of growth of Lerch zeta functions},
  series = {Mathematics},
  volume    = {11},
  journal   = {Mathematics},
  number    = {3},
  issn      = {2227-7390},
  doi       = {10.3390/math11030723},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-303981},
  year      = {2023},
  abstract  = {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 Lindel{\"o}f hypothesis). The growth of an analytic function is closely related to the distribution of its zeros.},
  language  = {en}
}