On the functional properties of Bessel zeta-functions

• Autorzy: Takumi Noda
• Języki publikacji: EN

Abstrakty

EN

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).

Kategorie tematyczne

• 11M41: Other Dirichlet series and zeta functions
• 11F11: Holomorphic modular forms of integral weight

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2015
• Tom: 171
• Numer: 1
• Strony: 1-13

Daty

wydano

2015

Twórcy

autor

Takumi Noda

• College of Engineering, Nihon University, 1 Nakagawara, Tokusada, Tamuramachi, Koriyama, Fukushima 963-8642, Japan

Identyfikatory

DOI

10.4064/aa171-1-1