Trevor Wooley

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Trevor Wooley is affiliated with the following schools: University of York, University of Bristol, Imperial College London, University of Michigan, Purdue University

Trevor Wooley's AcademicInfluence.com Rankings

Trevor Wooley

Mathematics

#3442

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#5079

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Measure Theory

#2827

World Rank

#3365

Historical Rank

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Mathematics

Why Is Trevor Wooley Influential?

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According to Wikipedia, Trevor Dion Wooley FRS is a British mathematician and currently Professor of Mathematics at Purdue University. His fields of interest include analytic number theory, Diophantine equations and Diophantine problems, harmonic analysis, the Hardy-Littlewood circle method, and the theory and applications of exponential sums. He has made significant breakthroughs on Waring's problem, for which he was awarded the Salem Prize in 1998.

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Trevor Wooley'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

Vinogradov's mean value theorem via efficient congruencing, II (2011) (136)
The cubic case of the main conjecture in Vinogradov's mean value theorem (2014) (134)
Large improvements in Waring's problem (1992) (107)
Nested efficient congruencing and relatives of Vinogradov's mean value theorem (2017) (99)
Waring's problem: A survey (2002) (80)
On the Waring–Goldbach Problem for Fourth and Fifth Powers (2001) (76)
Privacy Amplification and Non-malleable Extractors via Character Sums (2011) (71)
Further improvements in Waring's problem (1995) (71)
ON VINOGRADOV'S MEAN VALUE THEOREM (1992) (66)
The Asymptotic Formula in Waring's Problem (2012) (63)
On a certain nonary cubic form and related equations (1995) (47)
On Waring's problem: Three cubes and a sixth power (1995) (43)
On waring's problem : some refinements (1991) (41)
Breaking classical convexity in Waring's problem: Sums of cubes and quasi-diagonal behaviour (1995) (41)
On simultaneous additive equations II. (1991) (41)
Near-Optimal Mean Value Estimates for Multidimensional Weyl Sums (2012) (41)
New Estimates for Smooth Weyl Sums (1995) (39)
Slim Exceptional Sets For Sums of Four Squares (2002) (39)
Multiple recurrence and convergence along the primes (2010) (39)
Slim Exceptional Sets for Sums of Cubes (2002) (38)
Multigrade efficient congruencing and Vinogradov's mean value theorem (2013) (38)
A note on simultaneous congruences (1996) (37)
On Simultaneous Additive Equations, I (1991) (36)
NUMBER THEORY FOR THE MILLENNIUM III (2002) (36)
Waring's problem in function fields (2009) (35)
NEW ESTIMATES FOR WEYL SUMS (1995) (34)
The application of a new mean value theorem to the fractional parts of polynomials (1993) (34)
Further improvements in Waring's problem, IV: Higher powers (2000) (33)
A low-energy decomposition theorem (2015) (32)
Cubic diophantine inequalities (1982) (29)
Some remarks on Gauss sums associated with kth powers (1995) (29)
On the Local Solubility of Diophantine Systems (1998) (29)
Translation invariance, exponential sums, and Waring's problem (2014) (27)
APPROXIMATING THE MAIN CONJECTURE IN VINOGRADOV'S MEAN VALUE THEOREM (2014) (27)
On diophantine inequalities: Freeman's asymptotic formulae (2003) (26)
On exponential sums over smooth numbers. (1997) (25)
On the exponential sum over k–free numbers (1998) (24)
The quadratic Waring–Goldbach problem (2004) (24)
Some remarks on Vinogradov's mean value theorem and Tarry's problem (1996) (24)
On Waring's Problem for Cubes and Smooth Weyl Sums (2001) (23)
Additive representation in thin sequences, I: Waring's problem for cubes☆ (2001) (23)
Rational solutions of pairs of diagonal equations, one cubic and one quadratic (2014) (23)
Sums of two k th powers. (1995) (23)
On Vinogradov’s mean value theorem: strongly diagonal behaviour via efficient congruencing (2013) (22)
Further improvements in Waring’s problem, II: Sixth powers (1994) (22)
Discrete Fourier restriction via Efficient Congruencing (2016) (21)
The Hasse principle for pairs of diagonal cubic forms (2007) (21)
A NOTE ON SYMMETRIC DIAGONAL EQUATIONS (1993) (20)
Mean value estimates for odd cubic Weyl sums (2014) (20)
Additive representation in thin sequences, II: The binary Goldbach problem (2000) (20)
Perturbations of Weyl sums (2015) (20)
Relations between exceptional sets for additive problems (2010) (19)
Slim exceptional sets and the asymptotic formula in Waring’s problem (2003) (19)
Quasi-diagonal behaviour in certain mean value theorems of additive number theory (1994) (19)
On simultaneous additive equations, IV (1990) (18)
An explicit version of Birch's Theorem (1998) (18)
A special case of Vinogradov's mean value theorem (1997) (18)
On sums of powers of almost equal primes (2014) (18)
On strings of consecutive integers with no large prime factors (1998) (17)
A Birch–Goldbach theorem (2010) (17)
On the Waring–Goldbach problem for seventh and higher powers (2016) (16)
Sums of Two Squares in Short Intervals (2000) (16)
Sums of fourth powers and related topics (1999) (15)
On Waring's problem: two cubes and seven biquadrates (2000) (15)
On the Waring–Goldbach problem for eighth and higher powers (2015) (14)
Additive representation in thin sequences, III: asymptotic formulae (2001) (14)
Linear Spaces on Cubic Hypersurfaces, and Pairs of Homogeneous Cubic Equations (1997) (14)
Further improvements in Waring’s problem. Ill Eighth powers (1993) (13)
The Hasse principle for systems of diagonal cubic forms (2013) (13)
Pairs of cubic forms in many variables (2003) (13)
On Weyl’s inequality, Hua’s lemma, and exponential sums over binary forms (1999) (13)
On the paucity of non-diagonal solutions in certain diagonal diophantine systems (1997) (13)
ADDITIVE REPRESENTATION IN THIN SEQUENCES, VIII: DIOPHANTINE INEQUALITIES IN REVIEW (2009) (12)
Subconvexity for additive equations: pairs of undenary cubic forms (2012) (12)
The representation of integers by binary additive forms (1998) (12)
Rational points on complete intersections of higher degree, and mean values of Weyl sums (2010) (12)
Slim Exceptional Sets in Waring's Problem: One Square and Five Cubes (2002) (11)
On Waring's problem: some consequences of Golubeva's method (2012) (11)
On Weyl sums for smaller exponents (2010) (10)
A quasi-paucity problem (2002) (9)
Artin's conjecture for septic and unidecic forms (2008) (9)
SPARSE VARIANCE FOR PRIMES IN ARITHMETIC PROGRESSION (2011) (9)
Discrete Restriction for (x,x3) and Related Topics (2019) (9)
Sums of three cubes (2000) (8)
Hua's Lemma and Simultaneous Diagonal Equations (2002) (8)
The unrestricted variant of Waring's problem in function fields (2007) (8)
Sums of two cubes (1995) (8)
Exceptional Sets for Diophantine Inequalities (2012) (8)
Sums of three cubes, II (2015) (8)
An affine slicing approach to certain paucity problems (1996) (8)
Diophantine problems in many variables: the role of additive number theory (1999) (8)
On Waring's problem: two squares and three biquadrates (2012) (7)
Vinogradov systems with a slice off (2017) (7)
The paucity problem for simultaneous quadratic and biquadratic equations (1999) (7)
On Waring's problem for intermediate powers (2016) (7)
The addition of binary cubic forms (1998) (7)
ON WARING'S PROBLEM: TWO SQUARES, TWO CUBES AND TWO SIXTH POWERS (2012) (7)
Twins of k-free numbers and their exponential sum (2000) (7)
Additive representation in thin sequences, V: Mixed problems of Waring's type (2003) (7)
DAVENPORT'S METHOD AND SLIM EXCEPTIONAL SETS: THE ASYMPTOTIC FORMULAE IN WARING'S PROBLEM (2010) (6)
On sums of sixteen biquadrates (2005) (6)
Additive Representation in Thin Sequences, IV: Lower Bound Methods (2001) (6)
Asymptotic formulae for pairs of diagonal equations (2004) (6)
On Vinogradov's mean value theorem. II. (1993) (6)
The paucity problem for certain pairs of diagonal equations (2003) (6)
Sums and Differences of Two Cubic Polynomials (2000) (6)
Asymptotic Formulae for Pairs of Diagonal Cubic Equations (2011) (6)
The density of integral solutions for pairs of diagonal cubic equations (2007) (5)
On Waring’s problem: Three cubes and a minicube (2010) (5)
An instance where the major and minor arc integrals meet (2019) (5)
On Vu's thin basis theorem in Waring's problem (2003) (5)
The asymptotic formula in Waring’s problem: Higher order expansions (2013) (5)
On Waring's problem: a square, four cubes and a biquadrate (1999) (5)
The asymptotic formulae in Waring's problem for cubes (2010) (5)
Discrete Fourier restriction via efficient congruencing: basic principles (2015) (5)
On Pairs of Diagonal Quintic Forms (2002) (4)
Cubic moments of Fourier coefficients and pairs of diagonal quartic forms (2013) (4)
Correlation estimates for sums of three cubes (2014) (4)
NUMBER THEORY WITH AN EMPHASIS ON THE MARKOFF SPECTRUM (1993) (4)
Artin's Conjecture and systems of diagonal equations (2013) (4)
On sums of two cubes: an Ω₊-estimate for the error term (1998) (4)
Additive representation in thin sequences, VI: representing primes, and related problems (2002) (4)
Equidistribution of polynomial sequences in function fields, with applications (2013) (4)
ON A PROBLEM RELATED TO ONE OF LITTLEWOOD AND OFFORD (1991) (4)
Quasi-Diagonal Behaviour and Smooth Weyl Sums (2000) (4)
Weyl's inequality and exponential sums over binary forms (2000) (3)
A light-weight version of Waring's problem (2004) (3)
On Linnik's Conjecture: Sums of Squares and Microsquares (2013) (3)
Arithmetic harmonic analysis for smooth quartic Weyl sums: three additive equations (2015) (3)
Slim exceptional sets for sums of fourth and fifth powers (2002) (3)
A paucity problem associated with a shifted integer analogue of the divisor function (2021) (3)
Diophantine inequalities and quasi-algebraically closed fields (2010) (3)
Solvable points on smooth projective varieties (2015) (3)
Forms in many variables (1997) (3)
Additive representation in short intervals, I: Waring's problem for cubes (2004) (3)
A Superpowered Euclidean Prime Generator (2016) (3)
Paucity problems and some relatives of Vinogradov’s mean value theorem (2021) (3)
Additive Representation in Thin Sequences, VII: Restricted Moments of the Number of Representations (2008) (3)
Hua’s Lemma and Exponential Sums over Binary Forms (2001) (2)
Number fields and function fields: coalescences, contrasts and emerging applications (2015) (2)
Additive representation in short intervals, II: sums of two like powers (2015) (2)
ANNEXE TO THE GALLERY: AN ADDENDUM TO “ADDITIVE REPRESENTATION IN THIN SEQUENCES, THIN DIOPHANTINE INEQUALITIES IN REVIEW” (2013) (2)
Analytic Number Theory (2008) (2)
Non-malleable extractors via character sums (2011) (2)
Pairs Of Diagonal Quartic Forms: The Non-Singular Hasse Principle (2021) (2)
A NOTE ON SIMULTANEOUS CONGRUENCES, II: MORDELL REVISED (2010) (2)
On Waring's problem for larger powers (2022) (2)
Diophantine Methods for Exponential Sums, and Exponential Sums for Diophantine Problems (2003) (2)
Corrigendum: The Asymptotic Formula in Waring's Problem, Internat. Math. Res. Notices (2012), No. 7, 1485–1504 (2015) (2)
Subconvexity in Inhomogeneous Vinogradov Systems (2022) (2)
On simultaneous additive equations and Waring's problem (1990) (1)
The Fourth China-Japan Conference on Number Theory (2006) (1)
WARING ' S PROBLEM : A (2007) (1)
SMOOTH VALUES OF POLYNOMIALS (2017) (1)
Optimal mean value estimates beyond Vinogradov’s mean value theorem (2019) (1)
Subconvexity and the Hilbert-Kamke Problem (2022) (1)
On smooth Weyl sums over biquadrates and Waring’s problem (2021) (1)
Restriction theory and perturbations of Weyl sums (2016) (1)
Subconvexity in the inhomogeneous cubic Vinogradov system (2022) (1)
Sums of fifth powers and related topics (1998) (1)
Near-Optimal Mean Value Estimates for Multidimensional Weyl Sums (2013) (1)
Finite Abelian Groups via Congruences (2022) (0)
On the Waring–Goldbach problem for seventh and higher powers (2016) (0)
Pairs of Diagonal Quartic Forms: The Asymptotic Formulae (2022) (0)
Topics in Number Theory (1999) (0)
Solvable points on smooth projective varieties (2015) (0)
VINOGRADOV SYSTEMS WITH A SLICE OFF JULIA BRANDES AND TREVOR D. WOOLEY In memoriam (2017) (0)
Workshop: Analytic Number Theory Table of Contents (2014) (0)
A pr 2 01 4 Translation invariance , exponential sums , and Waring ’ s problem (2021) (0)
Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences: 356 (1738) (1998) (0)
A paucity problem for certain triples of diagonal equations (2021) (0)
Arithmetic statistics, discrete restriction, and Fourier analysis (2021) (0)
The Hasse principle for systems of diagonal cubic forms (2015) (0)
ANALYTIC NUMBER THEORY, VOL. 2 - PROCEEDINGS OF A CONFERENCE IN HONOR OF HEINI HALBERSTAM (1996) (0)
On Waring’s problem: Three cubes and a sixth power (2001) (0)
(2017). A low-energy decomposition theorem. Quarterly Journal of Mathematics , 68 (1), 207-226. (2016) (0)
Gauss-Dirichlet Conference held in Gottingen on June 20-24, 2005 (2007) (0)
Arithmetic in Shangri-La (2013) (0)
Partitio Numerorum: sums of a prime and a number of $k$-th powers (2022) (0)
The representation of almost all numbers as sums of unlike powers (2001) (0)
On smooth gaps between consecutive prime numbers (1999) (0)
fields and function fields: Coalescences, contrasts and emerging applications. (2015) (0)
Diophantine inequalities and quasi-algebraically closed fields (2012) (0)
On Waring's problem: beyond Freiman's theorem (2023) (0)
THE PAUCITY PROBLEM FOR CERTAIN SYMMETRIC DIOPHANTINE EQUATIONS (2022) (0)
The difficulty of the local solubility problem for additive equations (2003) (0)
(2019). Optimal mean value estimates beyond Vinogradov's mean value theorem. arXiv . (2019) (0)
N T ] 1 2 O ct 2 01 5 A LOW-ENERGY DECOMPOSITION THEOREM (2018) (0)
International Congress of Mathematicians, Beijing, August 20-28 2002 (2002) (0)
Additive representation in short intervals, II: sums of two like powers (2016) (0)
Rational Points on Algebraic Varieties, Luminy (2001) (0)
Coffee Coffee Coffee Coffee Coffee 1100-1200 (2012) (0)
CORRIGENDUM: ON VINOGRADOV'S MEAN-VALUE THEOREM (1993) (0)

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What Schools Are Affiliated With Trevor Wooley?

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