Wyniki wyszukiwania

1

Cyclotomic matrices and a limit formula for hₚ¯

100%

Girstmair K.

Acta Arithmetica

|

2001

|

tom 97

|

nr 2

129-155

2

The Galois module of a twisted element in the $p^m$-th cyclotomic field

100%

Girstmair K.

Acta Arithmetica

|

1992

|

tom 61

|

nr 4

399-403

3

Dedekind sums with predictable signs

100%

Girstmair K.

Acta Arithmetica

|

1998

|

tom 83

|

nr 3

283-295

4

The Galois relation x₁ = x₂+x₃ and Fermat over finite fields

100%

Girstmair K.

Acta Arithmetica

|

2006

|

tom 124

|

nr 4

357-370

5

On the trace of the ring of integers of an abelian number field

100%

Girstmair K.

Acta Arithmetica

|

1992

|

tom 62

|

nr 4

383-389

EN

Let K, L be algebraic number fields with K ⊆ L, and $O_K$, $O_L$ their respective rings of integers. We consider the trace map $T = T_{L/K} : L → K$ and the $O_K$-ideal $T(O_L) ⊆ O_K$. By I(L/K) we denote the group index} of $T(O_L)$ in $O_K$ (i.e., the norm of $T(O_L)$ over ℚ). It seems to be difficult to determine I(L/K) in the general case. If K and L are absolutely abelian number fields, however, we obtain a fairly explicit description of the number I(L/K). This is a consequence of our description of the Galois module structure of $T(O_L)$ (Theorem 1). The case of equal conductors $f_K = f_L$ of the fields K, L is of particular interest. Here we show that I(L/K) is a certain power of 2 (Theorems 2, 3, 4).

6

The Galois relation x₁ = x₂ + x₃ for finite simple groups

100%

Girstmair K.

Acta Arithmetica

|

2007

|

tom 127

|

nr 3

301-303

7

Linear relations between roots of polynomials

100%

Girstmair K.

Acta Arithmetica

|

1999

|

tom 89

|

nr 1

53-96

8

On the branch order of the ring of integers of an abelian number field

100%

Girstmair K.

Acta Arithmetica

|

1992

|

tom 62

|

nr 3

297-301

9

Generalized Dedekind sums, correlation of L-series, and the Galois module of cot(π/N)cot(mπ/N)

100%

Girstmair K.

Acta Arithmetica

|

2003

|

tom 107

|

nr 1

69-89

10

Corrigendum to the paper: "Linear relations between roots of polynomials" (Acta Arith. 89 (1999), 53-96)

100%

Girstmair K.

Acta Arithmetica

|

2003

|

tom 110

|

nr 2

203

11

The digits of 1/p in connection with class number factors

100%

Girstmair K.

Acta Arithmetica

|

1994

|

tom 67

|

nr 4

381-386

12

Zones of large and small values for Dedekind sums

100%

Girstmair K.

Acta Arithmetica

|

2003

|

tom 109

|

nr 3

299-308

13

On the l-divisibility of the relative class number of certain cyclic number fields

100%

Girstmair K.

Acta Arithmetica

|

1993

|

tom 64

|

nr 2

189-204

14

Some linear relations between values of trigonometric functions at kπ/n

100%

Girstmair K.

Acta Arithmetica

|

1997

|

tom 81

|

nr 4

387-398

15

On the arithmetic mean of Dedekind sums

64%

Girstmair K., Schoißengeier J.

Acta Arithmetica

|

2005

|

tom 116

|

nr 2

189-198

Ograniczanie wyników

15 Acta Arithmetica

15 Girstmair K.

1 Schoißengeier J.

1 2007

1 2006

1 2005

3 2003

1 2001

1 1999

1 1998

1 1997

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1 1993

3 1992

Cyclotomic matrices and a limit formula for hₚ¯

The Galois module of a twisted element in the $p^m$-th cyclotomic field

Dedekind sums with predictable signs

The Galois relation x₁ = x₂+x₃ and Fermat over finite fields

On the trace of the ring of integers of an abelian number field

The Galois relation x₁ = x₂ + x₃ for finite simple groups

Linear relations between roots of polynomials

On the branch order of the ring of integers of an abelian number field

Generalized Dedekind sums, correlation of L-series, and the Galois module of cot(π/N)cot(mπ/N)

Corrigendum to the paper: "Linear relations between roots of polynomials" (Acta Arith. 89 (1999), 53-96)

The digits of 1/p in connection with class number factors

Zones of large and small values for Dedekind sums

On the l-divisibility of the relative class number of certain cyclic number fields

Some linear relations between values of trigonometric functions at kπ/n

On the arithmetic mean of Dedekind sums