Geodesic
Estimate of the Hecke $L$-functions on the critical line
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 2, Tome 91 (1979), pp. 40-51

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Under certain restrictions an estimate of Hecke $L$-functions on the critical line is obtained. This estimate is analogous to the estimate $$ \zeta(1/2+it)\ll t^{1/6}\ln^ct $$ for the Riemann zeta-function. 
@article{ZNSL_1979_91_a3,
     author = {R. M. Kaufman},
     title = {Estimate of the {Hecke} $L$-functions on the critical line},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {40--51},
     publisher = {mathdoc},
     volume = {91},
     year = {1979},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1979_91_a3/}
}
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R. M. Kaufman. Estimate of the Hecke $L$-functions on the critical line. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 2, Tome 91 (1979), pp. 40-51. http://geodesic.mathdoc.fr/item/ZNSL_1979_91_a3/