Displaying similar documents to “Spectral invariant of the zeta function of the Laplacian on Sp ( r + 1 ) / Sp ( 1 ) × Sp ( r ) ”

On Bernoulli identities and applications.

Minking Eie, King F. Lai (1998)

Revista Matemática Iberoamericana

Similarity:

Bernoulli numbers appear as special values of zeta functions at integers and identities relating the Bernoulli numbers follow as a consequence of properties of the corresponding zeta functions. The most famous example is that of the special values of the Riemann zeta function and the Bernoulli identities due to Euler. In this paper we introduce a general principle for producing Bernoulli identities and apply it to zeta functions considered by Shintani, Zagier and Eie. Our results include...

Integral identities and constructions of approximations to zeta-values

Yuri V. Nesterenko (2003)

Journal de théorie des nombres de Bordeaux

Similarity:

Some general construction of linear forms with rational coefficients in values of Riemann zeta-function at integer points is presented. These linear forms are expressed in terms of complex integrals of Barnes type that allows to estimate them. Some identity connecting these integrals and multiple integrals on the real unit cube is proved.

On a semigroup of measures with irregular densities

Przemysław Gadziński (2000)

Colloquium Mathematicae

Similarity:

We study the densities of the semigroup generated by the operator - X 2 + | Y | on the 3-dimensional Heisenberg group. We show that the 7th derivatives of the densities have a jump discontinuity. Outside the plane x=0 the densities are C ∞ . We give explicit spectral decomposition of images of - X 2 + | Y | in representations.

Spectral radius formula for commuting Hilbert space operators

Vladimír Muller, Andrzej Sołtysiak (1992)

Studia Mathematica

Similarity:

A formula is given for the (joint) spectral radius of an n-tuple of mutually commuting Hilbert space operators analogous to that for one operator. This gives a positive answer to a conjecture raised by J. W. Bunce in [1].

The reciprocal of the beta function and G L ( n , ℝ ) Whittaker functions

Eric Stade (1994)

Annales de l'institut Fourier

Similarity:

In this paper we derive, using the Gauss summation theorem for hypergeometric series, a simple integral expression for the reciprocal of Euler’s beta function. This expression is similar in form to several well-known integrals for the beta function itself. We then apply our new formula to the study of G L ( n , ℝ ) Whittaker functions, which are special functions that arise in the Fourier theory for automorphic forms on the general linear group. Specifically, we deduce explicit integral...