Geodesic
A. F. Lavrik's truncated equations
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions, Tome 76 (1978), pp. 124-158 Cet article a éte moissonné depuis la source Math-Net.Ru

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By a new method, we obtain some known results of A. F. Lavrik (Dokl. Akad. Nauk SSSR, 171, No. 2, 278–280 (1966); Mat. Zametki, 2, No. 5, 475–482 (1967); Izv. Akad. Nauk SSSR, Ser. Mat., 30, No. 2, 433–448 (1966)) regarding the truncated functional equations of various $L$-functions. As an application, we give an estimate of Dedekind's zeta-function of an algebraic number field $K$ of degree $n\leqslant4$ $\zeta_K(\frac12+it)\ll t^{n/6}\log^ct$, $t>1$ and a similar estimate for $L$-series with grцssencharacters. The method of the paper allows us to consider fields of degree $n\leqslant12$. 
@article{ZNSL_1978_76_a6,
     author = {R. M. Kaufman},
     title = {A. {F.~Lavrik's} truncated equations},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {124--158},
     year = {1978},
     volume = {76},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1978_76_a6/}
}
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R. M. Kaufman. A. F. Lavrik's truncated equations. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions, Tome 76 (1978), pp. 124-158. http://geodesic.mathdoc.fr/item/ZNSL_1978_76_a6/