Yuri I. Manin, Matilde Marcolli
Published 2021-01-01Version 1
Arguably, the first bridge between vast, ancient, but disjoint domains of mathematical knowledge, - topology and number theory, - was built only during the last fifty years. This bridge is the theory of spectra in the stable homotopy theory. This connection poses the challenge: discover a new information in number theory using the developed independently machinery of homotopy theory. In this combined research/survey paper we suggest to apply homotopy spectra to the problem of distribution of rational points upon algebraic manifolds.
Comments: 72 pages amstex
The Diophantine equations $ x^{n}_{1} +x^{n}_{2} +...+x^{n}_{r_{1}}= y ^{n}_{1} +y^{n}_{2} +...+y^{n}_{r_{2}} $
On certain diophantine equations of diagonal type
Infinite products in number theory and geometry
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