Arithmetic calculus of Fourier transforms by Igusa local zeta functions
Arithmetic calculus of Fourier transforms by Igusa local zeta functions
We show the possibility of explicit calculation of the Fourier transforms of complex powers of relative invariants of some prehomogeneous vector spaces over <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="double-struck upper R"> <mml:semantics> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="double-struck">R</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">\mathbb {R}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> by using the explicit form of <inline-formula content-type="math/mathml"> …