Why Is G. H. Hardy Influential?
According to Wikipedia , Godfrey Harold Hardy was an English mathematician, known for his achievements in number theory and mathematical analysis. In biology, he is known for the Hardy–Weinberg principle, a basic principle of population genetics.
G. H. Hardy's Published Works
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1900 1910 1920 1930 1940 1950 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 5500 6000 6500 7000 7500 Published Papers An Introduction to the Theory of Numbers An Introduction to the Theory of Numbers MENDELIAN PROPORTIONS IN A MIXED POPULATION. Some problems of ‘Partitio numerorum’; III: On the expression of a number as a sum of primes Some properties of fractional integrals. I. Asymptotic Formulaæ in Combinatory Analysis Asymptotic formulae in combinatory analysis (584) A mathematician's apology Contributions to the theory of the riemann zeta-function and the theory of the distribution of primes Note on a theorem of Hilbert Weierstrass’s non-differentiable function The Theory of Numbers A maximal theorem with function-theoretic applications On the Convergence of Certain Multiple Series What is Mathematics? Inequalities (Cambridge Mathematical Library) (263) A Theorem Concerning Fourier Transforms The general theory of Dirichlet's series A Course of Pure Mathematics Some new properties of fourier constants The Mean Value of the Modulus of an Analytic Function ON HILBERT TRANSFORMS Some problems of diophantine approximation Tauberian Theorems Concerning Power Series and Dirichlet's Series whose Coefficients are Positive* The zeros of Riemann's zeta-function on the critical line Some problems of diophantine approximation Some properties of conjugate functions. A convergence criterion for Fourier series A Source Book in Mathematics Some properties of fractional integrals. II BILINEAR FORMS BOUNDED IN SPACE [p, q] Some Problems of Diophantine Approximation: The Lattice-Points of a Right-Angled Triangle Asymptotic Formulӕ for the Distribution of Integers of Various Types The General Theory Of Dirichlets Series (96) Properties of Logarithmico‐Exponential Functions On Dirichlet's Divisor Problem Some problems of 'Partitio numerorum'; I: A new solution of Waring`s problem (82) Contributions to the Arithmetic Theory of Series SOME INTEGRAL INEQUALITIES CONNECTED WITH THE CALCULUS OF VARIATIONS THEOREMS CONCERNING MEAN VALUES OF ANALYTIC OR HARMONIC FUNCTIONS Theorems Relating to the Summability and Convergence of Slowly Oscillating Series Notes on the Theory of Series (XII): On Certain Inequalities Connected with the Calculus of Variations The Approximate Functional Equation in the Theory of the Zeta-Function, with Applications to the Divisor-Problems of Dirichlet and Piltz Some problems of ‘Partitio numerorum’ (VI): Further researches in Waring's Problem Some Problems of “Partitio Numerorum”(V): A Further Contribution to the Study of Goldbach's Problem Some problems of Diophantine approximation: The lattice-points of a right-angled triangle. (Second memoir.) Some more theorems concerning Fourier series and Fourier power series The strong summability of Fourier series The Average Order of the Arithmetical Functions P(x) and δ(x) Notes on special systems of orthogonal functions (IV): the orthogonal functions of whittaker's cardinal series The Integration of Functions of a Single Variable Some Problems of Diophantine Approximation: A Remarkable Trigonometrical Series. On the representation of a number as the sum of any number of squares, and in particular of five On the fractional parts of the powers of a number (II) Elementary theorems concerning power series with positive coefficients and moment constants of positive functions. The Maximum of a Certain Bilinear Form A Further Note on the Converse of Abel's Theorem A Mathematician's Apology NOTES ON THE THEORY OF SERIES (XIX): A PROBLEM CONCERNING MAJORANTS OF FOURIER SERIES The Lattice Points of a Circle Notes on the Theory of Series (XIII): Some New Properties of Fourier Constants A New Proof of a Theorem on Rearrangements Riemann's Form of Taylor's Series Solution of the Cesàro summability problem for power-series and Fourier series Some inequalities satisfied by the integrals or derivatives of real or analytic functions Some problems of ‘Partitio Numerorum’: IV. The singular series in Waring’s Problem and the value of the number G (k) The Approximate Functional Equations for ζ(s) and ζ2(s) I.—MATHEMATICAL PROOF SELF-RECIPROCAL FUNCTIONS An Inequality for Hausdorff Means Some new convergence criteria for Fourier series (41) A Note on a Theorem Concerning Series of Positive Terms: Extract from a Letter On the Theory of Linear Integral Equations Notes on the theory of series (XXIV): a curious power-series On the Summability of Fourier's Series Prolegomena To a Chapter on Inequalities Notes on the Theory of Series (XI): On Tauberian Theorems Theorems concerning the summability of series by boreľs exponential method NOTES ON THE THEORY OF SERIES (XX): GENERALIZATIONS OF A THEOREM OF PALEY Notes on the Theory of Series (VII): On Young's Convergence Criterion for Fourier Series The Second Theorem of Consistency for Summable Series NOTES ON FOURIER SERIES (III): ASYMPTOTIC FORMULAE FOR THE SUMS OF CERTAIN TRIGONOMETRICAL SERIES A Remark on Fourier Transforms The Indian Mathematician Ramanujan Some Results Concerning the Behaviour at Infinity of a Real and Continuous Solution of an Algebraic Differential Equation of the First Order Note on Ramanujan's arithmetical function τ (n) On the Representation of a Number as the Sum of any Number of Squares, and in Particular of five or seven. On the Coefficients in the Expansions of Certain Modular Functions Theorems concerning Mean Values of Analytic Functions A Note on Two Inequalities Transactions of the Cambridge Philosophical Society Some Problems of “Partitio Numerorum” (VIII): The Number Γ(k) in Waring's Problem The Multiplication of Conditionally Convergent Series Note on the theory of series (XXIII): On the partial sums of Fourier series A Class of Fourier Kernels The mean value of modulus of analytic functions (22) The Constants of Certain Inequalities Notes on the Theory of Series (XVI): Two Tauberian Theorems Two Theorems Concerning Fourier Series Notes on the Theory of Series (XVII) : Some New Convergence Criteria for Fourier Series Some problems of “partitio numerorum”: II. Proof that every large number is the sum of at most 21 biquadrates An Extension of a Theorem on Oscillating Series Some Theorems Concerning Trigonometrical Series of a Special Type Note on the equation Notes on the Theory of Series (IV): On the Strong Summability of Fourier Series Notes on the Theory of Series (XX): On Lambert Series Fourier Series On Hausdorff's methods of summability. II Eratosthenian Averages Notes on special systems of orthogonal Functions (III): A System of orthogonal polynomials Some new cases of Parseval's theorem On two theorems of F. Carlson and S. Wigert The Allied Series of a Fourier Series Abel's Theorem and its Converse Note on Lebesgue's Constants in the Theory of Fourier Series Summation of a Series of Polynomials of Laguerre On the Zeroes of Certain Classes of Integral Taylor Series. Part II.—On The Integral Function ∑n=0∞xn(n+a)8n! and Other Similar Functions Miscellaneous notes on Australian Diptera. III (16) Notes on the Theory of Series (VIII): An Inequality Notes on the Theory of Series (XV): On the Series Conjugate to the Fourier Series of a Bounded Function On subordinate functions Remarks in Addition to Dr. Widder's Note on Inequalities Some problems of ‘Partitio Numerorum’: IV. The singular series in Waring's Problem and the value of the numberG(k) Some problems of diophantine approximation: The analytic character of the sum of a dirichlet’ s series considered by hecke On a Tauberian Theorem for Lambert's Series, and Some Fundamental Theorems in the Analytic Theory of Numbers Notes on the Theory of Series (XVIII): on the Convergence of Fourier Series On a Class of Analytic Functions A further note on Ramanujan's arithmetical function τ( n) Notes on Fourier series (IV): Summability ( R 2 ) On lindelöfs hypothesis concerning the riemann zeta-function A Theorem Concerning Trigonometrical Series A note on a differential equation Theorems concerning functions subharmonic in a strip Solutions of Some Integral Equations Considered by Bateman, Kapteyn, Littlewood, and Milne Theorems Concerning Cesàro Means of Power Series Theorems Connected with Maclaurin's Test for the Convergence of Series Abel's Theorem and its Converse (II) William Henry Young Note on a Theorem of Mertens The Relations Between Borel's and Cesàro's Methods of Summation The Integral 0 ∞ sin x x dx A theorem on finite differences with an application to the theory of Hausdorff summability Fourier's series and analytic functions Notes on the Theory of Series (IX) : On the Absolute Convergence of Fourier Series Notes on Special Systems of Orthogonal Functions (II): On Functions Orthogonal with Respect to their Own Zeros Some problems of diophantine approximation: An additional note on the trigonometrical series associated with the elliptic theta-functions Notes on Fourier series (V): Summability ( R1) Cambridge Tracts in Mathematics and Mathematical Physics. No. 11. The Fundamental Theorems of the Differential Calculus A Formula of Ramanujan Notes on Two Theorems of Norbert Wiener The Theory of Cauchy's Principal Values. (Third Paper: Differentiation and Integration of Principal Values.) The Continuum and the Second Number Class The Theory of Cauchy's Principal Values. (Fourth Paper: The Integration of Principal Values—Continued—with Applications to the Inversion of Definite Integrals) An Introduction to the Study of Integral Equations. M. Bôcher. (Cambridge Tracts in Mathematics and Mathematical Physics, No. 10.) On the Zeroes Certain Classes of Integral Taylor Series. Part I.—On the Integral Function ∑n=0∞xφ(n){φ(n)}! Remarks on Three Recent Notes in the Journal Notes on the Theory of Series (XXII): On the Tauberian Theorem for Borel Summability Note on a Divergent Series A revision of the Chiromyzini (Diptera) The J-type and the S-type among Mathematicians THE SUMMABILITY OF A FOURIER SERIES BY LOGARITHMIC MEANS A Method for Determining a Behaviour of Certain Classes of Power Series Near a Singular Point on the Circle of Convergence Australian Bombyliidae and Cyrtidae (Diptera) (6) Notes on Tasmanian Diptera and description of new species Notes on the Theory of Series (V) : On Parseval's Theorem On the zeroes of certain integral functions (6) On an Integral Equation Notes on Moduli and Mean Values A Theorem Concerning Harmonic Functions Generalisation of a Theorem in the Theory of Divergent Series A Course of Pure Mathematics 3rd ed (6) Notes on Australian and exotic sarcophagid flies (6) Some theorems concerning infinite series Presidential Address: The Case against the Mathematical Tripos The Application to Dirichlet's Series of Borel's Exponential Method of Summation 484. Further Remarks on the Integral 0 ∞ sinx x dx On the Summability of Series by Borel's and Mittag-Leffler's Methods Miscellaneous notes on Australian Dipterap IXp Superfamily Asiloidea (5) A preliminary revision of some genera belonging to the Diptera Brachycera of Australia A Note on the Continuity or Discontinuity of a Function Defined by an Infinite Product Some Problems of Diophantine Approximation: The Series Σ e (λn) and the Distribution of the Points (λn α) Bertrand Russell and Trinity (5) A revision of the Australian Chiromyzini (Stratiomyiidae Diptera) (5) Notes on genus Calliphora lDipterarp Classificationc synonymyc distribution and phylogeny (5) Notes on the Theoey of Series—II: The Fourier Series of a Positive Function Notes on Australian Muscoidea (Calyptrata) (5) A Revision of the Australian Díptera belonging to the Genus Sarcophaga. (5) Third contribution towards a new classification of Australian Asilidae (4) Notes on Australian Bombyliidae, mostly from the manuscript papers of the late Arthur White (4) List of the Tenison Woods types of recent mollusca in the Tasmanian Museum (4) Leudesdorf's Extension of Wolstenholme's Theorem Some new Australian Sarcophagid flies and notes on others (4) The Resultant of Two Fourier Kernels Remarks on Some Points in the Theory of Divergent Series The Elementary Theory of Cauchy's Principal Values A Theorem in the Theory of Summable Divergent Series Some Extensions to Multiple Series of Abel's Theorem on the Continuity of Power Series What Is Geometry? (Presidential Address to the Mathematical Association, 1925) Ernest William Hobson Miscellaneous notes on Australian Diptera. XII. Cyrtidae, Dolichopodidae and Phoridae (4) Miscellaneous notes on Australian Diptera VI Dolichopodinae (3) External Genitalia of the Diptera Ergaste ou la vocation coloniale (3) XLVII.—TheAsilidæof Australia.—Part I Some Sarcophagid flies from Lord Howe Island Theoretische Arithmetik. (II. Abtheilung) On a theorem of Paley and Wiener 1844. A Mathematical Theorem about Golf Über die monotone Konvergenz der Cesàro-Mittel bei Fourier- und Potenzreihen Notes on the Theory of Series (X) : Some More Inequalities Additional Note on Two Problems in the Analytic Theory of Numbers G . H . HARDY AND PROBABILITY ? ? ? (3) The Theory of Cauchy's Principal Values. (Second Paper: The use of Principal Values in some of the Double Limit Problems of the Integral Calculus.) Second Note on a Theorem of Mertens An integral equation Properties of a Class of Double Intergrals RAMANUJAN AND THE THEORY OF FOURIER TRANSFORMS Notes on Fourier Series (I): On Sine Series with Positive Coefficients On the Symmetries of the Solutions of a Certain Variational Problem A Blowfly and some Parasites. (3) Australian Rhyphidae and Leptidae (Diptera) Raymond Edward Alan Christopher Paley Descriptions of some Australian flies belonging to the Diptera Brachycera Further notes on a new classification of Australian robberflies (Diptera - Asilidae) (3) On the type localities of certain flies described by Macquart in "Diptères Exotiques," supplement four (3) The Queensland Species of Calliphora subgenus Neopollenia Formulae Connecting Different Classes of Self-Reciprocal Functions An inequality Solution of An Integral Equation Note on Lambert's Series The wing venation of Lomatiinae (Diptera - Bombyliidae) (2) Notes on the Theory of Series (VI) : Two Inequalities Proof of a theorem of Paley A problem in the summation of series A Formula of Ramanujan in the Theory of Primes Einleitung in die Funktionentheorie, (1 Abteilung), von O. Stolz und I. A. Gmeiner. 1904. Some Theorems Connected with Abel's Theorem on the Continuity of Power Series Prof. E. W. Hobson, F.R.S. Notes on the theory of series (III): On the summability of the Fourier series of a nearly continuous function Miscellaneous notes on Australian Dipterap VIIIp Subfamily Lomatiinae (2) Some Notes on Certain Theorems in Higher Trigonometry Notes on Fourier Series (II): On the Gibbs Phenomenon The International Research Council An additional note on Parseval's theorem Observations regarding the Life-cycle o£ certain Australian Blowflies. (2) Australian Nemestrinidae (Diptera) (2) XIX.—Notes on the distribution of some West Australian Asilidæ XIII.—On the genus Damaromyia, Kertesz (Stratiomyiidæ) Some Australian Species of Calliphora (Subgenera Neopollenia and Proekon). Errata: “On the representation of a number as the sum of any number of squares, and in particular of five” [Trans. Amer. Math. Soc. 21 (1920), no. 3, 255–284; 1501144] Notes on the Theory of Series (XIV): An Additional Note on the Summability of Fourier Series The Fecundity of Mormoniella and some Problems in Parthenogenesis. (2) XIII.—The Asilidæ of Australia.—Part III Descriptions of Australian flies of the family Asilidae [Diptera], with synonyms and notes A new classification of Australian robberflies belonging to the subfamily Dasypogoninae lDipterac Asilidaer (2) Notes on the Sarcophaga peregrina Group (Dipt.) Miscellaneous notes on Australian Dipterap Xp Distributionc classification and the Tabanus posticus-group (2) The Sarcophaginae of Australia and New Zealand (2) Notes on Tasmanian Diptera and descriptions of new species, etc. I.—TheAsilidæof Australia.—Part II On Nicod's reduction in the number of primitives of logic [Mr S. Ramanujan's mathematical work in England : report (2) A Note on Parseval's Theorem for Fourier Transforms Lectures by Godfrey H. Hardy on the mathematical work of Ramanujan, fall term 1936 (2) Notes on flies of the genus Pelecorhynchus Tabanidae Prof. W. H. Young, F.R.S. The Ordinal Relations of the Terms of a Convergent Sequence On certain expansions of the solutions of the general Lamé equation On the Multiplication of Dirichlet's Series UPDATES ON A 1903 THEOREM OF (1) The Annual Meeting of the Mathematical Association—Report of the Council for 1925 A General Theorem Concerning Absolutely Convergent Series Additional Note on Certain Integral Equations New Solution of an Integral Equation Addendum: Summation of a Series of Polynomials of Laguerre Bertrand Russell & Trinity : a college controversy of the last war (1) Note on the Multiplication of Series A Point in the Theory of Conjugate Functions Another Formula of Ramanujan Inequalities satisfied by a certain definite integral Note in Addition to a Former Paper on Conditionally Convergent Multiple Series Note on the multiplication of series by Cauchy's rule Corrigendum: Leudesdorf's Extension of Wolstenholme's Theorem† John Raymond Wilton Miscellaneous notes on Australian Dipterap XIp Evolution of characters in the orderc venation of the Nemestrinidae (1) Notes on Australian Plies of the genus Calliphora. (1) Two new Australian species of Pollenia (1) Notes on Australian Muscoidea. VI. Calliphora in Australia and New Zealand (1) XLII.—TheAsilidæof Australia.—Part IV Notes on Sarcophaginae in India and Australia. (1) On the phylogeny of some Diptera Brachycera (1) On the male genitalia of some robber-flies belonging to the subfamily Asilinae [Diptera] A new gall-making thrips Australian Mydaidae (Diptera) (1) Miscellaneous notes on Australian Diptera. XV. Tabanus, Heteropsilopus (1) William Henry Young, 1863 - 1942 The Singular Points of Certain Classes of Functions of Several Variables S. Ramanujan, F.R.S. Einleitung in die Funktionentheorie, (I Abteilung) A Synonymie List of some described Australian Calliphorine Mies. (0) Two new Methods used in the Breeding and Preparing of Maggots for Medical Purposes. (0) Nutrition in the French Colonies. (0) Australian Dolichopodidae (Diptera) (0) Notes on Tasmanian butterflies (0) Miscellaneous back page (0) 999 Putnam Exam Problems' Solutions (0) Example to illustrate a Point in the Theory of Dirichlet's Series (0) Chapter II: Elementary theory of the convergence of Dirichlet's series (0) 319. To Find an Approximation to the Large Positive Root of the Equation Junior Teaching Appointments at Universities A System of Linear Equations with an Infinity of Unknowns On the Roots of the Equation 1Γ(x+1)=c Introduction to the Infinitesimal Calculus 225. The Line at Infinity, Etc. Chapter IV: The summation of series by typical means (0) Records of Proceedings at Meetings: Session November, 1926-June, 1927. Thursday, 10 February, 1927 Die complexen Veranderlichen und ihre Funktionen 1104. A Problem in Elementary Probability The book of the fly, a nature study of the house-fly and its kin, the fly plague and a cure, with an Introduction by Halford Ross. Chapter VIII: The multiplication of Dirichlet's series (0) On the zeroes of certain integral Taylor series : on the integral function (0) A Double Integral Records of Proceedings at Meetings Session November, 1926‐June, 1927 N. J.|Lobatschefskij’s Imaginäre Geometrie und Anwendung der Imaginären Geometrie auf einige Integrale. Herausgegeben von H. Liebmann. (Teubner, 1904; Pp. xi, 188.) On Error-correcting Balanced Codes, Ieee on Codes Satisfying Mth Order Running Digital Binary Transmission Codes with Higher Order Spec- Matched Spectral-null Codes for Partial-response Chan (0) On the Singularities of Functions Defined by Taylor's Series (Remarks in addition to a former Paper) Chapter III: The formula for the sum of the coefficients of a Dirichlet's series: The order of the function represented by the series (0) Chapter VII: Further developments of the theory of functions represented by Dirichlet's series (0) Some Identities Satisfied By Infinite Series Records of Proceedings at Meetings Thursday, 13 January, 1927 224. A Curious Imaginary Curve Inequalities Ed. 1st (0) Chapter VI: Abelian and Tauberian theorems (0) Prof. H. L. Lebesgue, For.Mem.R.S. Mersenne's Numbers 223. Higher Trigonometry Some Problems of Diophantine Approximation: The Series Sigma e (lambdan) and the Distribution of the Points (lambdan alpha). (0) The Cost of Scientific Publications. Thomas John Fanson Bromwich Addenda and Corrigenda 439. The Definition of a Complex Number Notes on Special Systems of Orthogonal Functions (I): The Boundedness of the Generalized Laguerre System l'Some problems of diophantine approximation’, acta mathematica Chapter V: General arithmetic theorems concerning typical means (0) A new Tasmanian butterfly and a list of the known Tasmanian species Twelfth Annual Report of the Walter and Eliza Hall Fellow in Economic Biology. (0) Report of Walter & Eliza Hall Fellow in Economic Biology. (0) Notes on the genus Pelecorhynchus (0) Miscellaneous notes on Australian Diptera. VII. On body-colour; and on species of Tabanidae, Cyrtidae and Asiloidea (0) Some Problems of Diophantine Approximation The Series and the Distribution of the Points (1916)(en)( (0) Walter & Eliza Hall Fellow in Economic Biology. (0) A description of Heterometopia argentea Macquart (Diptera Dexiidae) Notes on Tasmania Díptera and Descriptions of New Species. 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