Riv. Mat. Univ. Parma, Vol. 7, No. 1, 2016

Danilo Bazzanella[1]

Integer polynomials with small integrals

Pages: 165-179
Accepted in revised form: 18 March 2016
Mathematics Subject Classification (2010): 11C08, 11A41.
Keywords: Integer polynomials, Chebyshev problem, Prime counting function.
[1] : Dipartimento di Scienze Matematiche, Politecnico di Torino, Corso Duca degli Abruzzi 24, Torino 10129, Italy

Abstract: The smart method of Gelfond-Shnirelman-Nair allows to obtain in elementary way a lower bound for the prime counting functions $$\pi(x)$$ and $$\psi(x)$$, in terms of the integral of suitable integer polynomials. A survey on the knowledge about the method together with a new approach and some new results are presented.

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