Avner Ash

Q: What Schools Are Affiliated With Avner Ash

Avner Ash is affiliated with the following schools: University of Missouri, Boston College, University of Georgia, Harvard University

Avner Ash's AcademicInfluence.com Rankings

Avner Ash

Mathematics

#5641

World Rank

#7929

Historical Rank

Measure Theory

#2855

World Rank

#3396

Historical Rank

mathematics Degrees

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Mathematics

Why Is Avner Ash Influential?

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According to Wikipedia, Avner Ash is a professor of mathematics at Boston College. Ash received his Ph.D. from Harvard University in 1975 under the supervision of David Mumford. In 2012, Ash became a fellow of the American Mathematical Society.

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Avner Ash's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Smooth Compactification of Locally Symmetric Varieties (1975) (570)
Modular forms in characteristic $\ell$ and special values of their $L$ -functions (1986) (117)
Cohomology of arithmetic groups and congruences between systems of Hecke eigenvalues. (1986) (107)
The modular symbol and continued fractions in higher dimensions (1979) (81)
Galois representations with conjectural connections to arithmetic cohomology (2001) (78)
Small-dimensional classifying spaces for arithmetic subgroups of general linear groups (1984) (76)
An analogue of Serre's conjecture for Galois representations and Hecke eigenclasses in the mod p$ co (1999) (67)
Computations of cuspidal cohomology of congruence subgroups of SL(3, Z) (1984) (60)
Deformation retracts with lowest possible dimension of arithmetic quotients of self-adjoint homogeneous cones (1977) (58)
Galois representations attached to $\mod p$ cohomology of $GL(n,\mathbb{Z})$ (1992) (56)
Vanishing periods of cusp forms over modular symbols (1993) (51)
p-Adic deformations of arithmetic cohomology (2008) (48)
p-adicL-functions for GL(2n) (1994) (46)
ON THE COHOMOLOGY OF CONGRUENCE SUBGROUPS OF SL4(Z) (2002) (46)
Experimental Indications of Three-dimensional Galois Representations from the Cohomology of SL(3, Z) (1992) (42)
MODULAR FORMS IN CHARACTERISTIC ’ ANDSPECIAL VALUES OF THEIR L-FUNCTIONS (39)
Cohomology of Congruence Subgroups of SL_4(Z). III (2000) (38)
Unstable Cohomology of SL(n,O) (1994) (34)
Cohomology of congruence subgroups of SL(n, ℤ) (1980) (33)
p-adic deformations of cohomology classes of subgroups of GL (n, Z) (1997) (29)
Non-square-integrable cohomology of arithmetic groups (1980) (26)
Galois Representations, Hecke Operators, and the mod-p Cohomology of GL(3, Z) with Twisted Coefficients (1998) (24)
An A4 extension of Q attached to a non-selfdual automorphic form on GL(3). (1991) (23)
On Eutactic Forms (1977) (23)
ON THE GROWTH OF TORSION IN THE COHOMOLOGY OF ARITHMETIC GROUPS (2016) (22)
Cohomology at infinity and the well-rounded retract for general linear groups (1996) (22)
Cohomology of congruence subgroups of SL4(ℤ). III (2009) (21)
Parabolic Cohomology of Arithmetic Subgroups of SL(2, Z ) with Coefficients in the Field of Rational Functions on the Riemann Sphere (1989) (21)
Equality of Polynomial and Field Discriminants (2007) (21)
Resolutions of the Steinberg module for GL(n) (2011) (20)
Generalized modular symbols (1990) (20)
TORSION IN THE COHOMOLOGY OF CONGRUENCE SUBGROUPS OF SL(4, Z) AND GALOIS REPRESENTATIONS (2010) (19)
Moment problems and the causal set approach to quantum gravity (2002) (19)
On the Existence of Eutactic Forms (1980) (18)
Rigidity of p‐adic cohomology classes of congruence subgroups of GL(n, ℤ) (2006) (18)
An $$\widehat{A_4 }$$ extension of ℚ attached to a non-selfdual automorphic form onGL(3) (1991) (17)
Farrell cohomology of GL(n,Z) (1989) (14)
Modular Representations of GL(3, Fp), Symmetric Squares, and Mod-p Cohomology of GL(3, Z) (1999) (14)
Doubly cuspidal cohomology for principal congruence subgroups of GL(3, Z) (1992) (13)
Galois representations and cohomology of GL(n, ℤ) (1992) (13)
A note on minimal modular symbols (1986) (12)
EVERYWHERE UNRAMIFIED AUTOMORPHIC COHOMOLOGY FOR SL3(ℤ) (2008) (12)
Reducible Galois Representations and the Homology of GL(3, ℤ) (2012) (9)
Smooth Compactifications of Locally Symmetric Varieties: Frontmatter (2010) (9)
SL3 (F2)-Extensions of Q and Arithmetic Cohomology Modulo 2 (2004) (9)
Elliptic Tales: Curves, Counting, and Number Theory (2012) (8)
Random partial orders, posts, and the causal set approach to discrete quantum gravity (2005) (8)
Smooth Compactifications of Locally Symmetric Varieties: Compactifications of locally symmetric varieties (2010) (8)
Direct sums of mod p characters of Gal ( Q̄ / Q ) and the homology of GL n ( Z ) (2010) (7)
Non-minimal modular symbols for GL(n) (1988) (7)
Homological vanishing for the Steinberg representation (2017) (7)
Frequencies of Successive Pairs of Prime Residues (2011) (6)
Mod 2 Homology For GL(4) And Galois Representations (2013) (6)
Direct Sums of Mod p Characters of Gal and the Homology of GL(n, ℤ) (2013) (6)
DRAFT: P -ADIC DEFORMATIONS OF COHOMOLOGY CLASSES OF SUBGROUPS OF GL(N,Z): THE NON-ORDINARY CASE (2000) (6)
Hecke $L$ -Functions and the Distribution of Totally Positive Integers (2007) (5)
Comparison of Steinberg modules for a field and a subfield (2018) (4)
A6-extensions of Q and the modp cohomology of GL3(Z)☆ (2005) (4)
Smooth Compactifications of Locally Symmetric Varieties: Preface to the second edition (2010) (4)
Galois representations and Hecke operators associated with the mod- cohomology of (1997) (4)
Fearless Symmetry: Exposing the Hidden Patterns of Numbers (2006) (4)
Monomial Galois representations and Hecke eigenclasses in the mod-p cohomology of $GL((p-1),\mathbb{Z})$ (1999) (4)
Generalized modular symbols and relative Lie algebra cohomology (1996) (3)
Cohomology with twisted one-dimensional coefficients for congruence subgroups of SL4(Z) and Galois representations (2018) (3)
GALOIS REPRESENTATIONS AND HECKE OPERATORS ASSOCIATED WITH THE MOD p COHOMOLOGY OF GL(1,Z) AND GL(2,Z) (1997) (3)
Generalized Non‐Abelian Reciprocity Laws: a Context for Wiles' Proof (2000) (3)
Relaxation of strict parity for reducible Galois representations attached to the homology of GL(3, ℤ) (2016) (3)
Mod p cohomology of SL(n, Z) (1992) (3)
On the top betti number of subgroups of SL(n, ℤ) (1983) (3)
A constructive approach to p-adic deformations of arithmetic homology (2011) (2)
Hecke Operators and the Stable Homology of GL(n) (2012) (2)
Cohomology of subgroups of finite index of $SL\left( {3,Z} \right)$ and $SL\left( {4,Z} \right)$ (1977) (2)
Steinberg homology, modular forms, and real quadratic fields (2020) (2)
PARITY OF MOD p BETTI NUMBERS (1999) (2)
Galois representations and Hecke operators associated with the mod- $p$ cohomology of $GL(m(p-1),\mathbb{Z})$ (1998) (2)
Highly reducible Galois representations attached to the homology of (,ℤ) (2015) (2)
Smith theory and Hecke operators (2003) (1)
Non-vanishing of alternants☆ (2005) (1)
Reducible Galois representations and arithmetic homology for \protect \mathrm{GL}(4) (2018) (1)
Lattice-Packing by Spheres and Eutactic Forms (2019) (1)
Polyhedral reduction theory in self-adjoint cones (2010) (1)
Galois representations attached to tensor products of arithmetic cohomology (2016) (1)
Frequencies of Successive Tuples of Frobenius Classes (2009) (1)
Sums of Galois representations and arithmetic homology (2019) (0)
CHAPTER 10. COUNT THE WAYS (2016) (0)
HECKE L-FUNCTIONS, EISENSTEIN SERIES, AND THE DISTRIBUTION OF TOTALLY POSITIVE INTEGERS (2004) (0)
CHAPTER 16. MORE THEORY OF MODULAR FORMS (2016) (0)
CHAPTER 3. SUMS OF THREE AND FOUR SQUARES (2016) (0)
CHAPTER 8. CAST OF CHARACTERS (2016) (0)
Chapter 16. Frobenius (2008) (0)
Abstracts For Southern New England Conference on Quadratic Forms and Modular Forms (2016) (0)
Introduction: What is this book about? (2016) (0)
Cohomology of congruence subgroups of SL_3(Z), Steinberg modules, and real quadratic fields (2021) (0)
Chapter 7. Quadratic Reciprocity (2008) (0)
CHAPTER 4. SUMS OF HIGHER POWERS: WARING’S PROBLEM (2016) (0)
Chapter 14. The Restriction Morphism (2008) (0)
Chapter 6. Equations and Varieties (2008) (0)
Chapter 7. Abelian Groups (2015) (0)
A_6-extensions of Q and the mod p cohomology of GL(3,Z) (2004) (0)
NON-VANISHING OF ALTERNANTS by Avner Ash (2004) (0)
Chapter 17. Reciprocity Laws (2008) (0)
Chapter 9. Singular Cubics (2015) (0)
Chapter 11. Building Functions (2015) (0)
Chapter 15. The Conjecture of Birch and Swinnerton-Dyer (2015) (0)
Chapter 19. Quadratic Reciprocity Revisited (2008) (0)
A T ] 2 7 N ov 2 01 7 Homological vanishing for the Steinberg representation (2018) (0)
Summing It Up: From One Plus One to Modern Number Theory (2016) (0)
CHAPTER 14. CONGRUENCE GROUPS (2016) (0)
Chapter 1. Representations (2008) (0)
Chapter 14. Surprising Properties of L-functions (2015) (0)
Chapter 3. Permutations (2008) (0)
Homological stability for a sequence of groups and homomorphisms (2017) (0)
Chapter 5. Complex Numbers (2008) (0)
SL (2, Z) WITH COEFFICIENTS IN THE FIELD OF RATIONAL (2016) (0)
CHAPTER 12. MODULAR FORMS (2016) (0)
Even Galois representations and the cohomology of $$\mathrm{GL}(2,\mathbb Z)$$GL(2,Z) (2018) (0)
CHAPTER 5. SIMPLE SUMS (2016) (0)
CHAPTER 17. MORE THINGS TO DO WITH MODULAR FORMS: APPLICATIONS (2016) (0)
Chapter 3. The Projective Plane (2015) (0)
NEW DEFINITIONS OF CONTINUITY (2015) (0)
CHAPTER 13. HOW MANY MODULAR FORMS ARE THERE (2016) (0)
Chapter 2. Algebraic Closures (2015) (0)
CHAPTER 1. PROEM (2016) (0)
CHAPTER 11. THE UPPER HALF-PLANE (2016) (0)
Even Galois representations and the cohomology of GL(2,Z)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm{GL}(2 (2017) (0)
Chapter 18. One- And Two-Dimensional Representations (2008) (0)
Chapter 6. Transition to Elliptic Curves (2015) (0)
Chapter 22. Fermat’s Last Theorem and Generalized Fermat Equations (2008) (0)
Chapter 2. Groups (2008) (0)
Chapter 4. Modular Arithmetic (2008) (0)
Toward an explicit eigencurve for GL(3) (2017) (0)
Cohomology of congruence subgroups of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"><mml:msub><mml:mrow><mml:mi mathvariant="normal">SL</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mi mathvariant="double-stru (2022) (0)
Smooth Compactifications of Locally Symmetric Varieties: Further developments (2010) (0)
Chapter 10. Elliptic Curves over Q (2015) (0)
Chapter 21. A Last Look at Reciprocity (2008) (0)
Prime Numbers and the Riemann Hypothesis by Barry Mazur and William Stein (2018) (0)
Chapter 9. Elliptic Curves (2008) (0)
Chapter 12. Group Representations (2008) (0)
Chapter 5. Bézout’s Theorem (2015) (0)
Set theoretic Hida projectors (2008) (0)
Smooth Compactifications of Locally Symmetric Varieties: Basics on torus embeddings; examples (2010) (0)
CHAPTER 7. INFINITE SERIES (2016) (0)
CHAPTER 2. SUMS OF TWO SQUARES (2016) (0)
Chapter 10. Matrices (2008) (0)
Chapter 13. L-functions (2015) (0)
Smooth Compactifications of Locally Symmetric Varieties: Supplementary Bibliography (2010) (0)
Chapter 8. Galois Theory (2008) (0)
Chapter 1. Degree of a Curve (2015) (0)
Chapter 20. A Machine for Making Galois Representations (2008) (0)
Preface To The Paperback Edition (2008) (0)
Chapter 12. Analytic Continuation (2015) (0)
Chapter 13. The Galois Group Of A Polynomial (2008) (0)
Chapter 4. Multiplicities and Degree (2015) (0)
Chapter 8. Nonsingular Cubic Equations (2015) (0)
CHAPTER 9. ZETA AND BERNOULLI (2016) (0)
Chapter 23. Retrospect (2008) (0)
Chapter 11. Groups of Matrices (2008) (0)
A constructive approach to p-adic deformations of arithmetic homology (2011) (0)
St Reading Everywhere Unramified Automorphic Cohomology for Sl 3 (z) 1. Statement and Explanation of the Conjecture (2008) (0)
CHAPTER 6. SUMS OF POWERS, USING LOTS OF ALGEBRA (2016) (0)
Chapter 15. The Greeks Had a Name for it (2008) (0)
CHAPTER 15. PARTITIONS AND SUMS OF SQUARES REVISITED (2016) (0)

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What Schools Are Affiliated With Avner Ash?

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