Geodesic
Kummer's tower and big zeta-functions
Zapiski Nauchnykh Seminarov POMI, Algebra and number theory. Part 1, Tome 469 (2018), pp. 151-159

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The statement of the problem to construct a big zeta function is discussed. This problem is related to an arithmetic Hurwitz formula. Two pretenders to play the role of the big zeta are suggested. Representations and ramification structures, related to Kummer's tower, are studied. 
@article{ZNSL_2018_469_a5,
     author = {A. L. Smirnov},
     title = {Kummer's tower and big zeta-functions},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {151--159},
     publisher = {mathdoc},
     volume = {469},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2018_469_a5/}
}
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A. L. Smirnov. Kummer's tower and big zeta-functions. Zapiski Nauchnykh Seminarov POMI, Algebra and number theory. Part 1, Tome 469 (2018), pp. 151-159. http://geodesic.mathdoc.fr/item/ZNSL_2018_469_a5/