The Zeta Function of an Algebraic Number Field and Some Applications

2016 ◽  
pp. 119-150
Author(s):  
Steve Wright
Keyword(s):  
Zeta Function ◽  
Number Field ◽  
Algebraic Number ◽  
Algebraic Number Field

scholarly journals On the Arithmetic of Pfaffians

1972 ◽  
Vol 47 ◽  
pp. 169-198 ◽  
Author(s):  
Jun-Ichi Igusa
Keyword(s):  
Zeta Function ◽  
Number Field ◽  
Jordan Algebra ◽  
Algebraic Number ◽  
Algebraic Number Field ◽  
Hermitian Matrices ◽  
Norm Form ◽  
Simple Jordan Algebra

In this paper, we shall supply proofs to the results announced in [2], pp. 74-75: we shall prove the Siegel formula for the Pfaffian of degree n over an algebraic number field and also determine the zeta function of the Pfaffian. In the appendix, we shall briefly discuss the non-split case where the Pfaffian is replaced by the norm form of the simple Jordan algebra of quaternionic hermitian matrices of degree n.

On correspondence between orders and ideals with a normal basis in cyclic subfields of Q(ξp) of a prime degree l

2010 ◽  
Vol 60 (6) ◽  
Author(s):  
Juraj Kostra
Keyword(s):  
Number Field ◽  
Algebraic Number ◽  
Algebraic Number Field ◽  
Normal Basis ◽  
Prime Degree ◽  
One To One

AbstractLet K be a tamely ramified cyclic algebraic number field of prime degree l. In the paper one-to-one correspondence between all orders of K with a normal basis and all ideals of K with a normal basis is given.

scholarly journals The trace-form of an algebraic number field

1973 ◽  
Vol 5 (5) ◽  
pp. 379-384 ◽  
Author(s):  
Donald Maurer
Keyword(s):  
Number Field ◽  
Algebraic Number ◽  
Algebraic Number Field ◽  
Trace Form

scholarly journals Automorphy factors for a Hilbert modular group

1988 ◽  
Vol 30 (2) ◽  
pp. 231-236
Author(s):  
Shigeaki Tsuyumine
Keyword(s):  
Number Field ◽  
Algebraic Number ◽  
Rational Number ◽  
Modular Group ◽  
Algebraic Number Field ◽  
Maximal Order ◽  
Hilbert Modular Group ◽  
Hilbert Modular ◽  
Totally Real

Let K be a totally real algebraic number field of degree n > 1, and let OK be the maximal order. We denote by гk, the Hilbert modular group SL2(OK) associated with K. On the extent of the weight of an automorphy factor for гK, some restrictions are imposed, not as in the elliptic modular case. Maass [5] showed that the weight is integral for K = ℚ(√5). It was shown by Christian [1] that for any Hilbert modular group it is a rational number with the bounded denominator depending on the group.

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