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Collected Papers of Srinivasa Ramanujan

Publisher: 
AMS/Chelsea
Number of Pages: 
426
Price: 
47.00
ISBN: 
0-8218-2076-1
Date Received: 
Tuesday, February 14, 2006
Reviewable: 
Yes
Include In BLL Rating: 
Yes
G. H. Hardy, P. V. Seshu Aiyar, and B. M. Wilson, editors
Publication Date: 
2000
Format: 
Hardcover
Category: 
Sourcebook
BLL
07/14/2009
BLL Rating: 

  • 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 $\pi$
  • On the integral $\int^x_0\frac{\tan^{-1}t}{t}dt$
  • On the number of divisors of a number
  • On the sum of the square roots of the first $n$ natural numbers
  • On the product $\prod^{n=\infty}_{n=0}[1+(\frac{x}{a+nd})^3]$
  • Some definite integrals
  • Some definite integrals connected with Gauss's sums
  • Summation of a certain series
  • New expressions for Riemann's functions $\xi(s)$ and $\Xi(t)$
  • 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 $\gamma$
  • On the expression of a number in the form $ax^2 + by^2 + cz^2 +du^2$
  • 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 formulæ 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
Publish Book: 
Modify Date: 
Tuesday, July 14, 2009

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