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