THE AMERICAN MATHEMATICAL SOCIETY

1942 Science  
In this paper we consider spaces of GL(4, R)-Whittaker functions, which are special functions that arise in the study of GL(4, R) automorphic forms. Our main result is to determine explicitly the series expansion for a GL(4, R)-Whittaker function that is "fundamental," in that it may be used to generate a basis for the space of all GL(4, K)-Whittaker functions of fixed eigenvalues. The series that we find in the case of GL(4, R) is particularly interesting in that its coefficients are not
more » ... ients are not merely ratios of Gamma functions, as they are in the lower-rank cases. Rather, these coefficients are themselves certain seriesnamely, they are finite hypergeometric series of unit argument. We suspect that this is a fair indication of what will happen in the general case of GL(n , R).
doi:10.1126/science.96.2496.399-b pmid:17735635 fatcat:3owfqvqjfzbn7insbkp2jo7crq