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Pair arithmetical equivalence for quadratic fields
- Source :
- Mathematische Zeitschrift
- Publication Year :
- 2020
-
Abstract
- Given two distinct number fields $K$ and $M$, and finite order Hecke characters $\chi$ of $K$ and $\eta$ of $M$ respectively, we say that the pairs $(\chi, K)$ and $(\eta, M)$ are arithmetically equivalent if the associated L-functions coincide: $$L(s, \chi, K) = L(s, \eta, M) .$$ When the characters are trivial, this reduces to the question of fields with the same Dedekind zeta function, investigated by Gassman in 1926, who found such fields of degree 180, and by Perlis (1977) and others, who showed that there are no nonisomorphic fields of degree less than $7$. We construct infinitely many such pairs where the fields are quadratic. This gives dihedral automorphic forms induced from characters of different quadratic fields. We also give a classification of such characters of order 2 for the quadratic fields of our examples, all with odd class number.<br />Comment: Added references to work of David Rohrlich. Accepted for publication
- Subjects :
- Degree (graph theory)
Mathematics - Number Theory
General Mathematics
010102 general mathematics
Automorphic form
Order (ring theory)
Algebraic number field
16. Peace & justice
01 natural sciences
11R42 (Primary) 11F80, 11F11 (Secondary)
Combinatorics
Quadratic equation
Number theory
0103 physical sciences
FOS: Mathematics
Arithmetic function
Number Theory (math.NT)
010307 mathematical physics
Representation Theory (math.RT)
0101 mathematics
Dedekind zeta function
Mathematics - Representation Theory
Mathematics
Subjects
Details
- Language :
- English
- Database :
- OpenAIRE
- Journal :
- Mathematische Zeitschrift
- Accession number :
- edsair.doi.dedup.....86ac08b71cf74425e21409f4605538ef