The Laplace transform of the functions tν(1+ t)β, Reν > −1, is expressed in terms of Whittaker functions. This expression is exploited to evaluate infinite integrals involving products of Bessel functions, powers, exponentials, and Whittaker functions. Some special cases of the result are discussed. It is also demonstrated that the famous identity ∫∞ 0 sin(ax)/xdx =π/2 is a special case of our ...

The matrix Whittaker kernel has been introduced by A. Borodin in Part IV of the present series of papers. This kernel describes a point process — a probability measure on a space of countable point configurations. The kernel is expressed in terms of the Whittaker confluent hypergeometric functions. It depends on two parameters and determines a J-symmetric operator K in L(R+)⊕ L(R+). It turns ou...

Let G = GSp(2) be the symplectic group with similitude of degree two, which is defined over Q. For a generic cusp form F on the adelized group GA which generates a large discrete series representation at infinity, we show that its spinor Lfunction is continued to an entire function and satisfies the functional equation. 0. Introduction. Let G = GSp(2) be the symplectic group with similitude of ...

Résumé Soit G un groupe réductif p-adique et U0 le radical unipotent d’un sousgroupe parabolique minimal de G. Nous introduisons une transformation de Fourier pour l’espace des fonctions de Whittaker lisses sur G et à support compact modulo U0. Nous en déterminons l’image. La preuve suit celle d’Heiermann pour les fonctions sur le groupe. Au cours de la preuve, une formule d’inversion est prouv...

1.1 One of the important technical tools in D. Gaitsgory’s proof of the Vanishing Conjecture appearing in the geometric Langlands correspondence ([3]) is the theory of Whittaker functors for GLn. In this paper we define analogous functors for GSp4 and study their properties. Let us first review the situation at the level of automorphic forms on G = Sp4. Let X be a smooth projective absolutely i...

Socio-Technical Lifelogging: Deriving Design Principles for a Future Proof Digital Past Steve Whittaker a , Vaiva Kalnikaitė b , Daniela Petrelli c , Abigail Sellen d , Nicolas Villar d , Ofer Bergman e , Paul Clough f & Jens Brockmeier g h a University of California at Santa Cruz b Interactables, Cambridge, United Kingdom c Sheffield Hallam University, United Kingdom d Microsoft Research Cambr...