Frobenius distributions in GL2-extensions: distribution of Frobenius automorphisms in GL2-extensions of the rational numbers
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
1976
|
| Series: | Lecture notes in mathematics
504 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 274 S. graph. Darst. |
| ISBN: | 354007550X 038707550X |
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| 245 | 1 | 0 | |a Frobenius distributions in GL2-extensions |b distribution of Frobenius automorphisms in GL2-extensions of the rational numbers |c Serge Lang ; Hale F. Trotter |
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Record in the Search Index
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|---|---|
| adam_text | 9
PARTI
SUPERSINGULAR AND FIXED TRACE DISTRIBUTION
PRELIMINARIES
1. The Galois representation in GL. 17
2. Some notions of probability 20
THE DISTRIBUTION FOR FIXED TRACE
3. The probabilistic model 29
4. The asymptotic behavior 33
EXAMPLES
5. Serre curves, M = 2q, the general formula 41
6. Computations of Galois groups 46
7. The curve y2 = x3 + 6x 2 51
8. The Shimura curve XQ(11) 55
10
PART II
IMAGINARY QUADRATIC DISTRIBUTION
Introduction 69
THE FIXED TRACE CASE
1. Fixed traces from the quadratic field 77
2. Computation of the constant for fixed trace 84
THE MODEL FOR THE MIXED CASE
3. The mixed Galois representations 91
4. The probabilistic model 104
5. The asymptotic behavior 108
6. The finite part of the constant as a quotient of integrals 112
COMPUTATIONS OF HARISH TRANSFORMS
7. Haar measure under the trace determinant map on Mat2.
General formalism. 123
8. Relations with the trace norm map on k 133
9. Computation of C^ for almost all I 141
10. The constant for Serre curves, K D kgb = Qab 143
11. The constant for XQ(ll) 149
11
PART III
SPECIAL COMPUTATIONS
Introduction 157
GENERAL LEMMAS
1. Lemmas on commutator subgroups 163
2. G2 , GL2(Z2) 165
3. Cases when K ( I kab = Qab 174
4. K n kab when k = Q(V^3) and GL2(Z3) splits 181
5. K D kgb in other cases 185
k = QCV^)
6. The action of Q on k(A1/3) 191
7. The constant for Serre fiberings, k = Q(V 3), M = 2q,
q odd prime ^ 3, A = ±q 195
8. Computation of integrals 201
k = Q(i)
9. The constant for Serre fiberings, q odd ^ 3 209
k = ?( /£¦)
10. The action of 3 on k(A2,A1/4) when k = Q(#) 215
11. The action of matrices on k(A4) 218
12. Computation of integrals and the constant 221
12
PART IV
NUMERICAL RESULTS
SUPERSINGULAR AND FIXED TRACE DISTRIBUTION
1. General discussion of results 235
2. Tables
Table I : Fixed trace distributions 239
Table II : Supersingular primes 240
Table III: Primes with t = 1 241
Table IV: Traces of Frobenius 242
IMAGINARY QUADRATIC DISTRIBUTION
3. General discussion of results 249
4. Tables
Table V : Imaginary quadratic distributions 253
Table VI : Primes associated with fields of small discriminant,
for curves A and B 258
Table VII: Distribution of primes associated with small
discriminants 260
EXTENDED RESULTS FOR XQ(11)
5. Discussion and description of tables 265
Table VIII: Supersingular primes 267
Table IX : Imaginary quadratic distribution 268
Table X : Distribution of primes for fields with small
discriminants 269
Remarks on the Computations 271
Bibliography 273
|
| any_adam_object | 1 |
| author | Lang, Serge 1927-2005 Trotter, Hale F. |
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| author_facet | Lang, Serge 1927-2005 Trotter, Hale F. |
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| dewey-ones | 512 - Algebra 510 - Mathematics |
| dewey-raw | 512/.7 510/.8 |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T15:38:00Z |
| institution | BVB |
| isbn | 354007550X 038707550X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001280290 |
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| physical | 274 S. graph. Darst. |
| publishDate | 1976 |
| publishDateSearch | 1976 |
| publishDateSort | 1976 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Lang, Serge 1927-2005 Verfasser (DE-588)119305119 aut Frobenius distributions in GL2-extensions distribution of Frobenius automorphisms in GL2-extensions of the rational numbers Serge Lang ; Hale F. Trotter Berlin [u.a.] Springer 1976 274 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 504 Extensions de corps (Mathématiques) Extensions de corps (mathématiques) ram Galois, Théorie de Galois, Théorie de ram Nombres rationnels Nombres rationnels ram Nombres, Théorie probabiliste des Nombres, Théorie probabiliste des ram Field extensions (Mathematics) Galois theory Numbers, Rational Probabilistic number theory Frobenius-Automorphismus (DE-588)4770758-6 gnd rswk-swf GL2-Erweiterung (DE-588)4770757-4 gnd rswk-swf Rationale Zahl (DE-588)4048495-6 gnd rswk-swf Rationale Zahl (DE-588)4048495-6 s GL2-Erweiterung (DE-588)4770757-4 s Frobenius-Automorphismus (DE-588)4770758-6 s DE-604 Trotter, Hale F. Verfasser aut Lecture notes in mathematics 504 (DE-604)BV000676446 504 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001280290&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lang, Serge 1927-2005 Trotter, Hale F. Frobenius distributions in GL2-extensions distribution of Frobenius automorphisms in GL2-extensions of the rational numbers Lecture notes in mathematics Extensions de corps (Mathématiques) Extensions de corps (mathématiques) ram Galois, Théorie de Galois, Théorie de ram Nombres rationnels Nombres rationnels ram Nombres, Théorie probabiliste des Nombres, Théorie probabiliste des ram Field extensions (Mathematics) Galois theory Numbers, Rational Probabilistic number theory Frobenius-Automorphismus (DE-588)4770758-6 gnd GL2-Erweiterung (DE-588)4770757-4 gnd Rationale Zahl (DE-588)4048495-6 gnd |
| subject_GND | (DE-588)4770758-6 (DE-588)4770757-4 (DE-588)4048495-6 |
| title | Frobenius distributions in GL2-extensions distribution of Frobenius automorphisms in GL2-extensions of the rational numbers |
| title_auth | Frobenius distributions in GL2-extensions distribution of Frobenius automorphisms in GL2-extensions of the rational numbers |
| title_exact_search | Frobenius distributions in GL2-extensions distribution of Frobenius automorphisms in GL2-extensions of the rational numbers |
| title_full | Frobenius distributions in GL2-extensions distribution of Frobenius automorphisms in GL2-extensions of the rational numbers Serge Lang ; Hale F. Trotter |
| title_fullStr | Frobenius distributions in GL2-extensions distribution of Frobenius automorphisms in GL2-extensions of the rational numbers Serge Lang ; Hale F. Trotter |
| title_full_unstemmed | Frobenius distributions in GL2-extensions distribution of Frobenius automorphisms in GL2-extensions of the rational numbers Serge Lang ; Hale F. Trotter |
| title_short | Frobenius distributions in GL2-extensions |
| title_sort | frobenius distributions in gl2 extensions distribution of frobenius automorphisms in gl2 extensions of the rational numbers |
| title_sub | distribution of Frobenius automorphisms in GL2-extensions of the rational numbers |
| topic | Extensions de corps (Mathématiques) Extensions de corps (mathématiques) ram Galois, Théorie de Galois, Théorie de ram Nombres rationnels Nombres rationnels ram Nombres, Théorie probabiliste des Nombres, Théorie probabiliste des ram Field extensions (Mathematics) Galois theory Numbers, Rational Probabilistic number theory Frobenius-Automorphismus (DE-588)4770758-6 gnd GL2-Erweiterung (DE-588)4770757-4 gnd Rationale Zahl (DE-588)4048495-6 gnd |
| topic_facet | Extensions de corps (Mathématiques) Extensions de corps (mathématiques) Galois, Théorie de Nombres rationnels Nombres, Théorie probabiliste des Field extensions (Mathematics) Galois theory Numbers, Rational Probabilistic number theory Frobenius-Automorphismus GL2-Erweiterung Rationale Zahl |
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