Geodesic
Non-real poles on the axis of absolute convergence of the zeta functions associated to Pascal’s triangle modulo a prime
Tomohiro Ikkai1
1 Graduate School of Mathematics Nagoya University 464-8602 Nagoya, Japan
Acta Arithmetica, Tome 178 (2017) no. 1, pp. 43-55.

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In Pascal’s triangle, the binomial coefficients not divisible by a given prime form a set with self-similarity. Essouabri studied a class of meromorphic functions associated to that set. These functions are related to fractal geometry and it is of interest whether such a function has a non-real pole on its axis of absolute convergence. Essouabri proved the existence of such a pole in the simplest case. The keys to his proof are Stein’s and Wilson’s estimates on how fast the points multiply in the above self-similar set. This article gives an extension of Essouabri’s result.
DOI : 10.4064/aa8359-9-2016
Keywords: pascal triangle binomial coefficients divisible given prime form set self similarity essouabri studied class meromorphic functions associated set these functions related fractal geometry interest whether function has non real pole its axis absolute convergence essouabri proved existence pole simplest keys his proof stein wilson estimates fast points multiply above self similar set article gives extension essouabri result

Tomohiro Ikkai 1

1 Graduate School of Mathematics Nagoya University 464-8602 Nagoya, Japan 
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Tomohiro Ikkai. Non-real poles on the axis of absolute convergence of the zeta functions associated to Pascal’s triangle modulo a prime. Acta Arithmetica, Tome 178 (2017) no. 1, pp. 43-55. doi : 10.4064/aa8359-9-2016. http://geodesic.mathdoc.fr/articles/10.4064/aa8359-9-2016/

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