On Unfoldings of Some Integrals of Automorphic Functions on General Linear Groups

2018/05/24 by Tsiokos, Eleftherios
#FOS: Mathematics #Group Theory (math.GR) #Number Theory (math.NT) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1805.09809

Abstract

We use results about Fourier coefficients appearing in [T] (and some more obtained here), to obtain information for certain among the integrals of the form I=∫_{GLn(\kkk)Zn(\A)\s GLn(\A)}φ(g)ϕ(g)\F(E)(\tj(g))dg where: \A is the adele ring of a number field \kkk; φ is a GL_n(\A)-cuspidal automorphic form; ϕ is a GL_n(\A)-automorphic function (even the trivial for some results); E is a GL_N(\A)-automorphic form for a multiple N of n; \F(E) is a Fourier coefficient of E for certain choices of additive functions \F in a set \BBnk[N] which we defined in [T]; \tj is a diagonal embedding of GL_n in GL_N; of course \tj(GL_n)∈\StabGL_N\F; and Z_n is the center of GL_n.

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