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Exploring Prime Numbers and Modular Functions I: On the Exponential of Prime Number via Dedekind Eta Function

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Abstract:

The main objective this paper is to develop asymptotic formulas for the exponential of prime number, using Dedekind eta function, and afterwards an elliptic modular function.

Info:

Periodical:
Bulletin of Mathematical Sciences and Applications (Volume 7)
Pages:
22-31
Citation:
E. Guedes and R. R. Gandhi, "Exploring Prime Numbers and Modular Functions I: On the Exponential of Prime Number via Dedekind Eta Function", Bulletin of Mathematical Sciences and Applications, Vol. 7, pp. 22-31, 2014
Online since:
Feb 2014
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References:

Cesàro, Ernest, Sur une formule empirique de M. Pervouchine, Comptes rendus hebdomadaires des séances de l'Academia des sciences 119: 848-849, (1894). (French).

Apostol, Tom M., Modular functions and Dirichlet series in number theory, Springer Verlag, (2000).

Iisstein, Eric W., Dedekind Eta Function, from MathWorld - A Wolfram Ib Resource, http: /mathworld. wolfram. com/DedekindEtaFunction. html, available in November 17, (2013).

Iber, Heinrich, Lehrbuch der Algebra, Vol. 3, (1908).

Andrews, George E. and Berndt, Bruce C., Ramanujan's Lost Notebook, Part II, Springer, 2009. καιδιζlκαιs.

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