2016, ISBN 9780691170190, xiii, 229

.... Mathematicians Avner Ash and Robert Gross explore addition's most basic characteristics as well as the addition of squares and other powers before moving onward to infinite series, modular forms...

Mathematics | Number theory | General | Counting & Numeration | Number Theory | Popular works

Mathematics | Number theory | General | Counting & Numeration | Number Theory | Popular works

Book

2012, ISBN 9780691151199, xvii, 253

.... In this book, Avner Ash and Robert Gross guide readers through the mathematics they need to understand this captivating problem...

Curves, Elliptic | Number theory | Elliptic functions | Mathematics | History & Philosophy | Abstract | PDZ | PBX | Calculus | PBKA | Geometry | Algebra | PBF | Algebraic | PBH | PBMW | Number Theory

Curves, Elliptic | Number theory | Elliptic functions | Mathematics | History & Philosophy | Abstract | PDZ | PBX | Calculus | PBKA | Geometry | Algebra | PBF | Algebraic | PBH | PBMW | Number Theory

Book

2006, ISBN 0691124922, xxv, 272

Mathematicians solve equations, or try to. But sometimes the solutions are not as interesting as the beautiful symmetric patterns that lead to them. Written in...

Number theory | Mathematics

Number theory | Mathematics

Book

Annales mathématiques du Québec, ISSN 2195-4755, 4/2019, Volume 43, Issue 1, pp. 1 - 35

...Annales mathématiques du Québec (2019) 43:1–35 https://doi.org/10.1007/s40316-018-0104-7 Even Galois representations and the cohomology of GL(2, Z) Avner Ash 1...

Galois representations | Algebra | Analysis | 11F80 | Mathematics, general | Arithmetic cohomology | Mathematics | Number Theory | 11F75

Galois representations | Algebra | Analysis | 11F80 | Mathematics, general | Arithmetic cohomology | Mathematics | Number Theory | 11F75

Journal Article

International Journal of Number Theory, ISSN 1793-0421, 06/2017, Volume 13, Issue 5, pp. 1213 - 1231

Starting with a numerically noncritical (at p ) Hecke eigenclass f in the homology of a congruence subgroup Γ of SL 3 ( ℤ ) (where p divides the level of Γ )...

MATHEMATICS | p-adic deformation | arithmetic group | Eigencurve | homology | COHOMOLOGY

MATHEMATICS | p-adic deformation | arithmetic group | Eigencurve | homology | COHOMOLOGY

Journal Article

International Journal of Number Theory, ISSN 1793-0421, 03/2016, Volume 12, Issue 2, pp. 361 - 381

In this paper, we prove the following theorem: Let be an algebraic closure of a finite field of characteristic p > 3 . Let ρ be a continuous homomorphism from...

Hecke operator | Galois representation | Serre's conjecture | MATHEMATICS | MODULAR-REPRESENTATIONS | MOD-P COHOMOLOGY | CONJECTURE

Hecke operator | Galois representation | Serre's conjecture | MATHEMATICS | MODULAR-REPRESENTATIONS | MOD-P COHOMOLOGY | CONJECTURE

Journal Article

The American Mathematical Monthly, ISSN 0002-9890, 05/2018, Volume 125, Issue 5, pp. 476 - 480

Journal Article

Acta Arithmetica, ISSN 0065-1036, 2011, Volume 149, Issue 4, pp. 305 - 319

P-adic | Homology | Deformations | Cohomology | Eigenvariety | Arithmetic | MATHEMATICS | eigenvariety | CONGRUENCE SUBGROUPS | homology | cohomology | deformations | arithmetic | p-adic

Journal Article

Parkinsonism and Related Disorders, ISSN 1353-8020, 2016, Volume 36, pp. 47 - 51

Abstract Objective Mutations in the GBA gene are associated with Parkinson's disease (PD). A definite description of the clinical characteristics of PD...

Neurology | Parkinson's disease | GBA | Gaucher's disease | GENOTYPE | RISK | ASHKENAZI JEWISH POPULATION | GLUCOCEREBROSIDASE MUTATIONS | CLINICAL NEUROLOGY | GAUCHER-DISEASE | Glucosylceramidase - genetics | Cross-Sectional Studies | Humans | Middle Aged | Male | Parkinson Disease - genetics | Mutation - genetics | Phenotype | Gaucher Disease - genetics | Aged, 80 and over | Parkinson Disease - diagnosis | Adult | Female | Aged | Gaucher Disease - diagnosis | Cohort Studies | Medical colleges | Neurosciences | Genetic aspects | Genes | Genetic research | Analysis

Neurology | Parkinson's disease | GBA | Gaucher's disease | GENOTYPE | RISK | ASHKENAZI JEWISH POPULATION | GLUCOCEREBROSIDASE MUTATIONS | CLINICAL NEUROLOGY | GAUCHER-DISEASE | Glucosylceramidase - genetics | Cross-Sectional Studies | Humans | Middle Aged | Male | Parkinson Disease - genetics | Mutation - genetics | Phenotype | Gaucher Disease - genetics | Aged, 80 and over | Parkinson Disease - diagnosis | Adult | Female | Aged | Gaucher Disease - diagnosis | Cohort Studies | Medical colleges | Neurosciences | Genetic aspects | Genes | Genetic research | Analysis

Journal Article

Journal of Algebra, ISSN 0021-8693, 08/2018, Volume 507, pp. 200 - 224

Let E/F be an extension of fields. We investigate the Steinberg module of GL(n,E) restricted to GL(n,F). We give examples for n=2 and n=3 where we compute the...

Arithmetic group | Steinberg representation | General linear group | MATHEMATICS

Arithmetic group | Steinberg representation | General linear group | MATHEMATICS

Journal Article

Experimental mathematics, ISSN 1058-6458, 06/2019, pp. 1 - 7

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 01/2020, Volume 373, Issue 1, pp. 273 - 293

Let \Gamma _0(n,N) denote the usual congruence subgroup of type \Gamma _0 and level N in \text {SL}(n,{\mathbb{Z}}). Suppose for i=1,2 that we have an...

MATHEMATICS | TORSION | GL(N | SUBGROUPS | MOD-P COHOMOLOGY

MATHEMATICS | TORSION | GL(N | SUBGROUPS | MOD-P COHOMOLOGY

Journal Article

1975, Lie groups, ISBN 9780915692125, Volume 4. 4, iv, 335

Book

06/2020

We compare the homology of a congruence subgroup Gamma of GL_2(Z) with coefficients in the Steinberg modules over Q and over E, where E is a real quadratic...

Mathematics - Number Theory

Mathematics - Number Theory

Journal Article

Communications in Algebra, ISSN 0092-7872, 05/2013, Volume 41, Issue 5, pp. 1751 - 1775

We prove the following theorem: Let be an algebraic closure of a finite field of characteristic p. Let ρ be a continuous homomorphism from the absolute Galois...

Hecke operator | Serre's conjecture | Character | Primary 11F75 | Secondary 11F67 | Galois representation | Algebra

Hecke operator | Serre's conjecture | Character | Primary 11F75 | Secondary 11F67 | Galois representation | Algebra

Journal Article

16.
Full Text
Torsion in the cohomology of congruence subgroups of SL(4,Z) and Galois representations

Journal of algebra, ISSN 0021-8693, 2011, Volume 325, Issue 1, pp. 404 - 415

We report on the computation of torsion in certain homology theories of congruence subgroups of SL ( 4 , Z ) . Among these are the usual group cohomology, the...

Galois representations | Cohomology of arithmetic groups | Hecke operators | Automorphic forms | Torsion cohomology classes | Secondary | Primary | MATHEMATICS | MOD-P COHOMOLOGY | CONJECTURE

Galois representations | Cohomology of arithmetic groups | Hecke operators | Automorphic forms | Torsion cohomology classes | Secondary | Primary | MATHEMATICS | MOD-P COHOMOLOGY | CONJECTURE

Journal Article

Communications in algebra, ISSN 0092-7872, 05/2013, Volume 41, Issue 5, pp. 1751 - 1775

Journal Article

2010, 2nd ed., Cambridge Mathematical Library, ISBN 9780521739559, 242

The new edition of this celebrated and long-unavailable book preserves the original book's content and structure and its unrivalled presentation of a universal...

Mathematics | Lie groups | Embeddings (Mathematics) | Symmetric spaces | Algebraic varieties

Mathematics | Lie groups | Embeddings (Mathematics) | Symmetric spaces | Algebraic varieties

eBook

Annales Mathematiques du Quebec, ISSN 2195-4755, 04/2019, Volume 43, Issue 1

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 09/2015, Volume 143, Issue 9, pp. 3801 - 3813

Let n\ge 1 and \mathbb{F} be an algebraic closure of a finite field of characteristic p>n+1. Let \rho :G_{\mathbb{Q}}\to \mathrm {GL}(n,\mathbb{F}) be a Galois...

Journal Article

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