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Modular Forms and Functions
1. Groups of matrices and bilinear mappings 2. Mapping properties 3. Automorphic factors and multiplier systems 4. General properties of modular forms 5. Construction of modular forms 6. Functions
Contributions to the theory of Ramanujan's function τ( n ) and similar arithmetical functions: II. The order of the Fourier coefficients of integral modular forms
Suppose thatis an integral modular form of dimensions −κ, where κ > 0, and Stufe N, which vanishes at all the rational cusps of the fundamental region, and which is absolutely convergent for
The Closest Packing of Spherical Caps in n Dimensions
  • R. Rankin
  • Mathematics
    Proceedings of the Glasgow Mathematical…
  • 1 July 1955
Let Sn denote the “surface” of an n-dimensional unit sphere in Euclidean space of n dimensions. We may suppose that the sphere is centred at the origin of coordinates O, so that the points P(x1, x2,
A Minimum Problem for the Epstein Zeta-Function
  • R. Rankin
  • Mathematics
    Proceedings of the Glasgow Mathematical…
  • 1 December 1953
In some recent work by D. G. Kendall and the author † on the number of points of a lattice which lie in a random circle the mean value of the variance emerged as a constant multiple of the value of
XXIV.—Sets of Integers Containing not more than a Given Number of Terms in Arithmetical Progression*
Sets of integers are constructed having the property that n members are in arithmetical progression only if they are all equal; here n is any integer greater than or equal to 3. Previous results have
Ramanujan: Letters and Commentary
A brief biography of Ramanujan Ramanujan in Madras (chapter 1) Ramanujan's first two letters to Hardy and Hardy's response (chapter 2) Preparing to go to England (chapter 3) Ramanujan at Cambridge
A campanological problem in group theory. II
1. The problem investigated in this note was suggested by a study of the mathematical basis of change ringing. Its campanological application is discussed in § 4.