William C. Waterhouse | Academic Influence

William C. Waterhouse's AcademicInfluence.com Rankings

William C. Waterhouse

Mathematics

#2664

World Rank

#4072

Historical Rank

#1037

USA Rank

Measure Theory

#1741

World Rank

#2138

Historical Rank

#560

USA Rank

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Mathematics

William C. Waterhouse's Degrees

PhD Mathematics University of California, Berkeley
Bachelors Mathematics University of California, Berkeley

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Why Is William C. Waterhouse Influential?

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According to Wikipedia, William Charles Waterhouse was an American mathematician. He was a professor emeritus of Mathematics at Pennsylvania State University, after having taught there for over 35 years. The early part of his career was at Cornell University. His research interests included abstract algebra, number theory, group schemes, and the history of mathematics.

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William C. Waterhouse'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

Introduction to Affine Group Schemes (1979) (859)
Abelian varieties over finite fields (1969) (299)
One-Dimensional Affine Group Schemes* (1980) (61)
Do Symmetric Problems Have Symmetric Solutions (1983) (55)
Automorphisms of det(Xij): The group scheme approach (1987) (46)
Principal homogeneous spaces and group scheme extensions (1971) (41)
Abstract homomorphisms of algebraic groups: problems and bibliography (1981) (37)
The codimension of singular matrix pairs (1984) (36)
Profinite groups are Galois groups (1974) (33)
The Normal Closures of Certain Kummer Extensions (1994) (33)
The structure of inseparable field extensions (1975) (33)
Basically bounded functors and flat sheaves. (1975) (31)
Projective modules over rings with many units (1981) (31)
Pairs of quadratic forms (1976) (30)
The discovery of the regular solids (1972) (29)
Gauss's first argument for least squares (1990) (27)
An empty inverse limit (1972) (23)
Moore's theorem on uniqueness of reciprocity laws (1972) (23)
Two generators for the general linear groups over finite fields (1989) (22)
On UC Spaces (1965) (22)
The early proofs of Sylow's theorem (1980) (21)
Pieces of eight in class groups of quadratic fields (1973) (20)
The new Langwill index: A dictionary of musical wind-instrument makers and inventors (1993) (20)
Dual groups of vector spaces (1968) (20)
Faithful Flatness of Hopf Algebras (1979) (18)
A unified Kummer-Artin-Schreier sequence (1987) (18)
The Stone-Weierstrass theorem for valuable fields. (1968) (18)
Automorphism schemes and forms of Witt Lie algebras (1971) (18)
The Number of Congruence Classes in Mn(Fq) (1995) (18)
Automorphisms of quotients of ΠGL(ni) (1982) (17)
Invertibility of linear maps preserving matrix invariants (1983) (16)
The absolute-value estimate for symmetric multilinear forms☆ (1990) (15)
How often do determinants over finite fields vanish? (1987) (15)
Automorphisms of GL n (R) (1980) (14)
The unit groups of affine algebraic monoids (1982) (14)
Geometrically reductive affine group schemes (1994) (13)
Self-adjoint operators and formally real fields (1976) (13)
Linear transformations preserving symmetric rank one matrices (1989) (11)
Differentiable functions on algebras and the equation grad (w) = M grad (v) (1992) (11)
Antipodes and group-likes in finite Hopf algebras (1975) (11)
Why Square Roots are Irrational (1986) (10)
Pairs of symmetric bilinear forms in characteristic $2$. (1977) (10)
Automorphisms and twisted forms of generalized Witt Lie algebras (1991) (9)
The structure of alternating-Hamiltonian matrices (2005) (9)
Scaled trace forms over number fields (1986) (9)
Linear maps preserving reduced norms (1982) (8)
Automorphisms of the Bruhat order on Coxeter Groups (1989) (8)
Linear transformations on self-adjoint matrices: the preservation of rank-one-plus-scalar (1986) (7)
A conjectured property of Hermitian pencils (1983) (7)
Real classification of complex quadrics (1982) (7)
Divisor classes in pseudo Galois extensions. (1971) (7)
A Counterexample for Germain (1994) (7)
Twisted forms of the determinant (1984) (6)
The Cimbasso and Related Instruments in 19th-Century Italy (1996) (6)
Maximal orders in nonassociative quaternion algebras (1992) (6)
Affine Group Schemes (1979) (6)
Circulant-style matrices closed under multiplication (1985) (6)
Discriminants of etale algebras and related structures. (1987) (6)
Notes toward higher differential algebra (1976) (6)
Similarity of matrices under SL(n,K) (1984) (6)
Review: Michiel Hazewinkel, Formal groups and applications (1982) (5)
Is it prayer, or is it parity? (2000) (5)
A NONSYMMETRIC HASSE-MINKOWSKI THEOREM.* (1977) (5)
Quadratic Polynomials and Unique Factorization (2002) (5)
On linear transformations preserving rank one matrices over commutative rings (1985) (5)
On p-Divisible Groups over Complete Valuation Rings (1972) (5)
Algebraic Matrix Groups (1979) (4)
Uniform Convergence and Graph Convergence (1976) (4)
On the Cattle Problem of Archimedes (1995) (4)
"The New Langwill Index. A dictionary of Wind-Instrument Makers and Inventors", William Waterhouse, London 1993 : [recenzja] / Ryszard Wieczorek. (1997) (4)
A probable Hasse principle for pencils of quadrics (1978) (4)
Automorphism group schemes of semisimple cosemisimple Hopf algebras (1993) (4)
Gauss on infinity (1979) (4)
The g-circulant solutions of Am=λJ (1987) (4)
A matrix maximum (1993) (4)
Composition of norm-type forms. (1984) (4)
A classification of almost full formal groups (1969) (4)
The map behind a binomial coefficient matrix over ZpZ (1988) (4)
Displacement operators relative to group matrices (1992) (4)
Affine Group Schemes: Examples (1979) (4)
Polynomial group laws over valuation rings (1982) (3)
The module structure of certain hopf algebra extensions (1982) (3)
Class groups of rings of invariants (1977) (3)
The density of supersingular Fermat varieties (1984) (3)
Early Double-Reeds (2001) (3)
Classifying nonsingular quadratic forms of rank three (1990) (3)
Automorphisms of _ (1980) (3)
Automorphism group schemes of basic matrix invariants (1995) (3)
When One Equation Solves Them All (1985) (3)
Symmetric determinants and Jordan norm similarities in characteristic 2 (1985) (3)
Retractions of separable commutative algebras (1993) (3)
The asymptotic density of supersingular Fermat varieties (1984) (3)
Tame objects for finite commutative Hopf algebras (1988) (3)
Square Root as a Homomorphism (2012) (3)
The degrees of the cyclotomic extension fields (1993) (3)
A unified version of the primitive and normal basis theorems (1994) (3)
Harmonic means and diophantus I.39 (1993) (2)
Nilpotent and Solvable Groups (1979) (2)
The sign of the Gaussian sum (1970) (2)
Eigenmatrices of a normal matrix (1997) (2)
The Unnamed God of the Pyrrha Ode (1987) (2)
A SPECIAL CASE OF POSITIVITY (2010) (2)
A tiny note on Gauss's Lemma (1988) (2)
A Conditional Trace Inequality (Paul A. Roediger) (1996) (2)
Composition and genera of norm-type forms (1984) (2)
Intersections of two cofinite subfields (2004) (2)
Shorter Notes: An Empty Inverse Limit (1972) (2)
A note by Gauss referring to ideals (1984) (2)
Elementary Problems: E2143-E2189 (1969) (2)
A note on fan's identity for symmetric bilinear forms (1987) (2)
Problems for Solution: E1641-E1650 (1963) (2)
The heights of formal $A$-modules (1974) (2)
Shorter Notes: Profinite Groups are Galois Groups (1974) (2)
A non-criterion for central simple algebras (1973) (2)
The structure of monomial circulant matrices (1987) (1)
Elementary divisors of s-symmetric matrices (1987) (1)
Polarization Formulas over Separable Algebras (1995) (1)
Advanced Problems: 6264-6266 (1979) (1)
Cochran's Theorem for Rings (2001) (1)
Linear operators on Clifford algebras (1994) (1)
The Proud Bassoon (1984) (1)
Inner product identities on the unit circle (1988) (1)
The Normal Basis Theorem (1979) (1)
The Words of the Second Sulpicia (1993) (1)
Not so much saffron, please. (2003) (1)
Review: Thomas Hawkins, Lebesgue's Theory of Integration, and Michael J. Crowe, A History of Vector Analysis, and I. Grattan-Guinness, The Development of the Foundations of Mathematical Analysis from Euler to Riemann, and Hans Wussing, Die Genesis des abstrakten Gruppenbegriffes (1972) (1)
The Double Flageolet - Made in England (1999) (1)
Some Errors in Applied Mathematics (1977) (1)
ORTHOGONAL SIMILARITY AND PAIRS OF QUADRATIC FORMS (1995) (1)
Subgroups of $ax+b$ and the splitting of triangular group schemes (1980) (1)
THE LOUSE IS BETTER: HEINSIUS AND JOHNSON (1994) (0)
Positivity properties in pencils of matrices (1986) (0)
A Unique Vector Sum (Rudolf K. Meyer) (1994) (0)
Irreducible and Connected Components (1979) (0)
Note. 'Insignia viralia' in the Memoirs of Martinus Scriblerus (1999) (0)
Book Review: The origins of Cauchy's rigorous calculus (1982) (0)
Extensions of complex number multiplication to 4-tuples (1992) (0)
An Amendatory Limerick (2008) (0)
Problems: 10184-10192 (1992) (0)
Local compactness of Hom (—, H) (2001) (0)
A Fact About Falling Bodies (1971) (0)
Integral ^1 by Ll Skew Circulants* (1986) (0)
AUTOMORPHISM GROUP SCHEMES OF SEMISIMPLE (2016) (0)
A Quotation from Moliére in Bentham (2005) (0)
The annihilator of a sum (1997) (0)
Advanced Problems: 5740-5745 (1970) (0)
‘INSIGNIA VIRALIA’ IN THEMEMOIRS OF MARTINUS SCRIBLERUS (1999) (0)
Quantifier problems beyond uniformity (1983) (0)
Descent Theory Formalism (1979) (0)
Review: Judith V. Grabiner, The origins of Cauchy's rigorous calculus, and Augustin Louis Cauchy, Équations différentielles ordinaires: Ordinary differential equations (1982) (0)
A Group of Invertible Matrices: 11186 (2007) (0)
Asymmetric linear correlations of projective planes over fields (2001) (0)
Elementary Problems: E3117-E3122 (1985) (0)
A Tag from Martial in Pepys's Diary (2004) (0)
Advanced Problems: 6619-6621 (1990) (0)
A Case of Flutes by Mr Bressan (1993) (0)
Connected Components and Separable Algebras (1979) (0)
Elementary Problems: E3282-E3288 (1988) (0)
An Urn Problem with Labeled and Unlabeled Balls: 11181. (2007) (0)
Construction of Quotients (1979) (0)
Real congruences of complex subspaces of 2 × 2 symmetric complex matrices (2006) (0)
Note on a method of extracting roots in as-Samaw'al (1978) (0)
Letter to the editor (1997) (0)
TAME OBJECTS FOR FINITE COMMUTATIVE (2010) (0)
An elementary interpretation of entry 12 in Gauss's Tagebuch (1991) (0)
Review: Mary-Claire van Leunen, A Handbook for Scholars (1979) (0)
A neglected note showing Gauss at work (1986) (0)
VANISHING THEOREMS FOR U-MANIFOLDS (2010) (0)
Advanced Problems: 5400-5409 (1966) (0)
OBSERVATION: A newly discovered 17th-century bassoon by Haka (1988) (0)
Emodulanda in Ovid’s Amores 1.1 (2008) (0)
Book Review: Formal groups and applications (1982) (0)
Orthogonal Matrices and the Matrix Exponential (Dennis S. Bernstein) (1991) (0)
The determination of all Carlitz sets (1989) (0)
Polynomials for the Jordan decomposition in characteristic p (2004) (0)
Descent Theory Computations (1979) (0)
Three study pieces for bassoon and piano (1969) (0)
More Reed Makers (1985) (0)
The New Langwill Index of Historical Wind-Instrument Makers (1988) (0)
Nonconstant Functions with Derivative Zero: 10772 (2000) (0)
Some Boundary Problems with Even or Odd Solutions (1996) (0)
Report on Galpin Society Visit to Lisbon (1988) (0)
LETTERS TO THE EDITOR (1982) (0)
Bhattacharyya’s matrix theorem (2013) (0)
Problem 11186 (2005) (0)
A Source for Johnson's 'Malim Cum Scaligero Errare' (2003) (0)
67.21 Visualising Cramer’s rule (1983) (0)
Polonaise for bassoon and piano (1969) (0)
Boswell, Joseph Warton, and Servius (2005) (0)
Extreme and Mean Ratio in Vergil (1972) (0)
The Glen Account Book - 1838-1853 (1986) (0)
Elementary Problems: E3093-E3098 (1985) (0)
The Style of the Bishop of Sodor and Man (2013) (0)
Sums of weight vectors and sums of semilinear functions (1988) (0)
How many vectors generate maximal cyclic subspaces (2003) (0)
A local determination theorem for finite principal homogeneous spaces (1991) (0)
Paoli Misremembering Cicero (2008) (0)
Book Review: Lebesgue's Theory of Integration (1972) (0)
Langwill and His Index (1986) (0)
Manuscripts and printed music (1985) (0)
Sonata in B flat major, K. 292 (1980) (0)
Groups of Multiplicative Type (1979) (0)
Problems for Solution: E1571-E1580 (1963) (0)
The Mathematical Experience and Mathematics Tomorrow (1983) (0)
Two Elementary Proofs of an Inequality (and 1½ Better Ones) (1989) (0)
Commutative polynomial group laws over valuation rings (1980) (0)
Music (1989) (0)
On the Ranks of Skew Centrosymmetric Matrices over Finite Fields (1998) (0)

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