On the functional properties of Bessel zeta-functions

Takumi Noda. "On the functional properties of Bessel zeta-functions." Acta Arithmetica 171.1 (2015): 1-13. <http://eudml.org/doc/279729>.

@article{TakumiNoda2015,
abstract = {Zeta-functions associated with modified Bessel functions are introduced as ordinary Dirichlet series whose coefficients are J-Bessel and K-Bessel functions. Integral representations, transformation formulas, a power series expansion involving the Riemann zeta-function and a recurrence formula are given. The inverse Laplace transform of Weber's first exponential integral is the basic tool to derive the integral representations. As an application, we give a new proof of the Fourier series expansion of the Poincaré series attached to SL(2,ℤ).},
author = {Takumi Noda},
journal = {Acta Arithmetica},
keywords = {Bessel zeta-function; Poincaré series; Ramanujan's formula},
language = {eng},
number = {1},
pages = {1-13},
title = {On the functional properties of Bessel zeta-functions},
url = {http://eudml.org/doc/279729},
volume = {171},
year = {2015},
}

TY - JOUR
AU - Takumi Noda
TI - On the functional properties of Bessel zeta-functions
JO - Acta Arithmetica
PY - 2015
VL - 171
IS - 1
SP - 1
EP - 13
AB - Zeta-functions associated with modified Bessel functions are introduced as ordinary Dirichlet series whose coefficients are J-Bessel and K-Bessel functions. Integral representations, transformation formulas, a power series expansion involving the Riemann zeta-function and a recurrence formula are given. The inverse Laplace transform of Weber's first exponential integral is the basic tool to derive the integral representations. As an application, we give a new proof of the Fourier series expansion of the Poincaré series attached to SL(2,ℤ).
LA - eng
KW - Bessel zeta-function; Poincaré series; Ramanujan's formula
UR - http://eudml.org/doc/279729
ER -