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On the Nature of γ-th Arithmetic Zeta Functions.
- Source :
-
Symmetry (20738994) . May2020, Vol. 12 Issue 5, p790. 1p. - Publication Year :
- 2020
-
Abstract
- Symmetry and elementary symmetric functions are main components of the proof of the celebrated Hermite–Lindemann theorem (about the transcendence of e α , for algebraic values of α) which settled the ancient Greek problem of squaring the circle. In this paper, we are interested in similar results, but for powers such as e γ log   n . This kind of problem can be posed in the context of arithmetic functions. More precisely, we study the arithmetic nature of the so-called γ-th arithmetic zeta function ζ γ (n) : = n γ ( = e γ log   n ), for a positive integer n and a complex number γ. Moreover, we raise a conjecture about the exceptional set of ζ γ , in the case in which γ is transcendental, and we connect it to the famous Schanuel's conjecture. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 20738994
- Volume :
- 12
- Issue :
- 5
- Database :
- Academic Search Index
- Journal :
- Symmetry (20738994)
- Publication Type :
- Academic Journal
- Accession number :
- 143544931
- Full Text :
- https://doi.org/10.3390/sym12050790