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Eleftherios Tsiokos

Publications and source records attributed to Eleftherios Tsiokos.

4 recordsLinked to original sources
arXiv2018

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

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 $$I=\int_{GL_n(\kkk)Z_n(\A)\s GL_n(\A)}φ(g)ϕ(g)\F(E)(\tj(g))dg$$ 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 $\tj(GL_n)\in\Stab{GL_N}{\F}$; and $Z_n$ is the center of $GL_n$.

math.NT↗
arXiv2018

On Fourier Coefficients of GL(n)-Automorphic Functions over Number Fields

We study Fourier coefficients of $GL_n(\A)$-automorphic functions $ϕ$, for $\A$ being the adele group of a number field $\kkk$. Let FC be an abbreviation for such a Fourier coefficient (and FCs for plural). Roughly speaking, in the present paper we process FCs by iteratively using the operations: Fourier expansions, certain exchanges of Fourier expansions, and conjugations. In Theorem 3.1 we express any FC in terms of---degenerate in many cases---Whittaker FCs. For FCs obtained from the trivial FC by choosing a certain "generic" term in each Fourier expansion involved, we establish a shortcut (Main corollary 6.17) for studying their expressions of the form in Theorem 3.1. The shortcut gives considerably less information, but it remains useful on finding automorphic representations so that for appropriate choices of $ϕ$ in them, the FC is factorizable and nonzero. Then in Theorems 8.3.11, 8.3.12, and 8.3.18, we study examples of FCs on which this shortcut applies, with many of them turning out to "correspond" to more than one unipotent orbit in $GL_n.$ For most of the paper, no knowledge on automorphic forms is necessary.

math.NT↗
arXiv2015

Convoluted Fourier Coefficients of GL(n)-Automorphic Functions. Part 1

We study certain cases of convoluted Fourier coefficients of $GL_n$-automorphic functions. We establish identities that express them in terms of Fourier coefficients related to unipotent orbits. The most general case that is studied is $(n)\circ(k,2^{n-1})$. The conclusions for this case is only up to a conjecture that I state. However there are certain special cases and other examples that are not based on any conjecture.

math.NT↗