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On the functional properties of Bessel zeta-functions

100%

Noda T.

Acta Arithmetica

2015

tom 171

nr 1

1-13

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).

An application of the projections of $C^{∞}$ automorphic forms

100%

Noda T.

Acta Arithmetica

1995

tom 72

nr 3

229-234

Ograniczanie wyników

2 Acta Arithmetica

2 Noda T.

1 2015

1 1995

Wyniki wyszukiwania

On the functional properties of Bessel zeta-functions

An application of the projections of $C^{∞}$ automorphic forms