@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}
}
@article{TongsompornWananiyakulSteuding2021,
  author    = {Tongsomporn, Janyarak and Wananiyakul, Saeree and Steuding, J{\"o}rn},
  title     = {The values of the periodic zeta-function at the nontrivial zeros of Riemann's zeta-function},
  series = {Symmetry},
  volume    = {13},
  journal   = {Symmetry},
  number    = {12},
  issn      = {2073-8994},
  doi       = {10.3390/sym13122410},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-252261},
  year      = {2021},
  abstract  = {In this paper, we prove an asymptotic formula for the sum of the values of the periodic zeta-function at the nontrivial zeros of the Riemann zeta-function (up to some height) which are symmetrical on the real line and the critical line. This is an extension of the previous results due to Garunkštis, Kalpokas, and, more recently, Sowa. Whereas Sowa's approach was assuming the yet unproved Riemann hypothesis, our result holds unconditionally.},
  language  = {en}
}