Contributors (Author(s), Editor(s), Translator(s), Illustrator(s) etc.)

G. H. Hardy, P. V. Seshu Aiyar, and B. M. Wilson

Table of Content

• Some properties of Bernoulli’s numbers
• On Question 330 of Prof. Sanjana
• Note on a set of simultaneous equations
• Irregular numbers
• Squaring the circle
• Modular equations and approximations to ∏
• On the integral  ∫^x₀tan−1t/t d t

• On the number of divisors of a number
• On the sum of the square roots of the first n natural numbers
• On the product ∏^n=∞_n=0[1+(x/a+nd)3]
• Some definite integrals
• Some definite integrals connected with Gauss’s sums
• Summation of a certain series
• New expressions for Riemann’s functions  ξ (s) and  Ξ(t)
• Highly composite numbers
• On certain infinite series
• Some formulæ in the analytic theory of numbers
• On certain arithmetical functions
• A series for Euler’s constant γ
• On the expression of a number in the form  ax²+by²+cz²+du²
• On certain trigonometrical sums and their applications in the theory of numbers
• Some definite integrals
• Some definite integrals
• A proof of Bertrand’s postulate
• Some properties of  p(n), the number of partitions of n
• Proof of certain identities in combinatory analysis
• A class of definite integrals
• Congruence properties of partitions
• Algebraic relations between certain infinite products
• Congruence properties of partitions
• Une formule asymptotique pour le nombre des partitions de n
• Proof that almost all numbers  n are composed of about  log log n prime factors
• Asymptotic formulæ in combinatory analysis
• Asymptotic formulæ for the distribution of integers of various types
• The normal number of prime factors of a number n
• Asymptotic formulae in combinatory analysis
• On the coefficients in the expansions of certain modular functions
• Questions and solutions
• Appendix I: Notes on the papers
• Appendix II: Further extracts from Ramanujan’s letters to G. H. Hardy
• Commentary on Ramanujan’s collected papers