Originally published in 1927, this book presents the collected papers of the renowned Indian mathematician Srinivasa Ramanujan (1887â 1920), with editorial contributions from G. H. Hardy (1877â 1947). Detailed notes are incorporated throughout and appendices are also included.
Originally published in 1927, this book presents the collected papers of the renowned Indian mathematician Srinivasa Ramanujan (1887â 1920), with editorial contributions from G. H. Hardy (1877â 1947). Detailed notes are incorporated throughout and appendices are also included.
Preface Notice P. V. Seshu and R. Bamachaundra Rao Notice G. H. Hardy Part I. Papers: 1. Some properties of Bernoulli's numbers 2. On question 330 of Prof. Sanjana 3. Note on a set of simultaneous equations 4. Irregular numbers 5. Squaring the circle 6. Modular equations and approximations to ¿ 7. On the integral [...] 8. On the number of divisors of a number 9. On the sum of the square roots of the first n natural numbers 10. On the product [...] 11. Some definite integrals 12. Some definite integrals connected with Gauss's sums 13. Summation of a certain series 14. New expression for Riemann's functions [...] 15. Highly composite numbers 16. On certain infinite series 17. Some formulae in the analytic theory of numbers 18. On certain arithmetical functions 19. A series of Euler's constant y 20. On the expression of a number in the form of ax2+by2+cz2+du2 21. On certain trigonometrical sums and their applications in the theory of numbers 22. Some definite integrals 23. Some definite integrals 24. A proof of Bertrand's postulate 25. Some properties of p (n), the number of partitions of n 26. Proof of certain identities in combinatory analysis 27. A class of definite integrals 28. Congruence properties of partitions 29. Algebraic relations between certain infinite products 30. Congruence properties of partitions 29. Algebraic relations between certain infinite products 30. Congruence properties of partitions Part II. Papers Written in Collaboration with G. H. Hardy: 31. Une formule asymptotique pour le nombre des partitions de n 32. Proof that almost all numbers n are composed of about log log n prime factors 33. Asymptotic formulae in combinatory analysis 34. Asymptotic formulae for the distribution of integers of various types 35. The normal number of prime factors of a number n 36. Asymptotic formulae in combinatory analysis 37. On the coefficients in the expansions of certain modular functions Questions and solutions Appendix 1. Notes on the papers Appendix 2. Further extracts from Ramanujan's letters to G. H. Hardy.
Preface Notice P. V. Seshu and R. Bamachaundra Rao Notice G. H. Hardy Part I. Papers: 1. Some properties of Bernoulli's numbers 2. On question 330 of Prof. Sanjana 3. Note on a set of simultaneous equations 4. Irregular numbers 5. Squaring the circle 6. Modular equations and approximations to ¿ 7. On the integral [...] 8. On the number of divisors of a number 9. On the sum of the square roots of the first n natural numbers 10. On the product [...] 11. Some definite integrals 12. Some definite integrals connected with Gauss's sums 13. Summation of a certain series 14. New expression for Riemann's functions [...] 15. Highly composite numbers 16. On certain infinite series 17. Some formulae in the analytic theory of numbers 18. On certain arithmetical functions 19. A series of Euler's constant y 20. On the expression of a number in the form of ax2+by2+cz2+du2 21. On certain trigonometrical sums and their applications in the theory of numbers 22. Some definite integrals 23. Some definite integrals 24. A proof of Bertrand's postulate 25. Some properties of p (n), the number of partitions of n 26. Proof of certain identities in combinatory analysis 27. A class of definite integrals 28. Congruence properties of partitions 29. Algebraic relations between certain infinite products 30. Congruence properties of partitions 29. Algebraic relations between certain infinite products 30. Congruence properties of partitions Part II. Papers Written in Collaboration with G. H. Hardy: 31. Une formule asymptotique pour le nombre des partitions de n 32. Proof that almost all numbers n are composed of about log log n prime factors 33. Asymptotic formulae in combinatory analysis 34. Asymptotic formulae for the distribution of integers of various types 35. The normal number of prime factors of a number n 36. Asymptotic formulae in combinatory analysis 37. On the coefficients in the expansions of certain modular functions Questions and solutions Appendix 1. Notes on the papers Appendix 2. Further extracts from Ramanujan's letters to G. H. Hardy.
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