Geodesic
Coincidence of $L$-functions
Yuta Katayama 1   ; Masanari Kida 1
1 Department of Mathematics Tokyo University of Science 1-3 Kagurazaka Shinjuku Tokyo 162-8601, Japan
Acta Arithmetica, Tome 204 (2022) no. 4, pp. 369-385 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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By the coincidence of $L$-functions, we mean an incident that the Hecke $L$-functions of ray class groups of several different fields coincide up to a finite number of Euler factors. This phenomenon was first observed by Hecke in 1925 for the case of quadratic fields. In this paper, we give a condition for the coincidence in the case of cyclic fields of prime degree in terms of Galois groups of certain abelian extension of the cyclic fields.
DOI : 10.4064/aa211012-14-6
Keywords: coincidence l functions mean incident hecke l functions ray class groups several different fields coincide finite number euler factors phenomenon first observed hecke quadratic fields paper condition coincidence cyclic fields prime degree terms galois groups certain abelian extension cyclic fields

Yuta Katayama  1   ; Masanari Kida  1

1 Department of Mathematics Tokyo University of Science 1-3 Kagurazaka Shinjuku Tokyo 162-8601, Japan 
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Yuta Katayama; Masanari Kida. Coincidence of $L$-functions. Acta Arithmetica, Tome 204 (2022) no. 4, pp. 369-385. doi: 10.4064/aa211012-14-6

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