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Congruences like Ramanujan's for powers of the partition function

✍ Scribed by Ian Kiming; Jørn B. Olsson

Publisher
Springer
Year
1992
Tongue
English
Weight
571 KB
Volume
59
Category
Article
ISSN
0003-889X

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📜 SIMILAR VOLUMES

On the Circular Summation of the Elevent
On the Circular Summation of the Eleventh Powers of Ramanujan's Theta Function
✍ Ken Ono 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 94 KB

Let f (a, b) denote Ramanujan's theta series. In his ``Lost Notebook'', Ramanujan claimed that the ``circular'' summation of n th powers of f satisfies a factorization of the form f (a n , b n ) F n (a n b n ) where F n (q)=1+2nq (n&1)Â2 + } } } . Moreover, he listed explicit closed formulas for F 2

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Zeros of the partition function for generalized ising systems
✍ Charles M. Newman 📂 Article 📅 1974 🏛 John Wiley and Sons 🌐 English ⚖ 641 KB

zj represents the external magnetic field at the j-th site and should not be confused with the activity variable used in the usual polynomial formulation of the Lee-Yang theorem.