scholarly journals Some problems of ?partitio numerorum?: II. Proof that every large number is the sum of at most 21 biquadrates

1921 ◽  
Vol 9 (1-2) ◽  
pp. 14-27 ◽  
Author(s):  
G. H. Hardy ◽  
J. E. Littlewood
Keyword(s):  
Partitio Numerorum

scholarly journals Euler's ``De Partitio Numerorum''

2007 ◽  
Vol 44 (04) ◽  
pp. 561-574 ◽  
Author(s):  
George E. Andrews
Keyword(s):  
Partitio Numerorum

Some problems of ?Partitio numerorum? (VI): Further researches in Waring's Problem

1925 ◽  
Vol 23 (1) ◽  
pp. 1-37 ◽  
Author(s):  
G. H. Hardy ◽  
J. E. Littlewood
Keyword(s):  
Waring’S Problem ◽  
Waring's Problem ◽  
Partitio Numerorum

THE RIEMANN ZETA FUNCTION AS AN EQUIVARIANT DIRAC INDEX

2012 ◽  
Vol 09 (08) ◽  
pp. 1250071 ◽  
Author(s):  
MAURO SPERA
Keyword(s):  
Zeta Function ◽  
Flat Space ◽  
Formal Similarity ◽  
The Riemann Zeta Function ◽  
Partitio Numerorum ◽  
Statistical Mechanical Model ◽  
Statistical Mechanical ◽  
Riemann Zeta ◽  
The One ◽  
Riemann’S Zeta Function

In this note an interpretation of Riemann's zeta function is provided in terms of an ℝ-equivariant L2-index of a Dirac–Ramond type operator, akin to the one on (mean zero) loops in flat space constructed by the present author and T. Wurzbacher. We build on the formal similarity between Euler's partitio numerorum function (the S1-equivariant L2-index of the loop space Dirac–Ramond operator) and Riemann's zeta function. Also, a Lefschetz–Atiyah–Bott interpretation of the result together with a generalization to M. Lapidus' fractal membranes are also discussed. A fermionic Bost–Connes type statistical mechanical model is presented as well, exhibiting a "phase transition at (inverse) temperature β = 1", which also holds for some "well-behaved" g-prime systems in the sense of Hilberdink–Lapidus.

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