Hecke eigenvalues and relations for Siegel Eisenstein series of arbitrary degree, level, and character
نویسندگان
چکیده
منابع مشابه
Siegel Eisenstein Series of Arbitrary Level and Theta Series
Introduction. In this paper we consider Siegel modular forms of genus n and arbitrary level q, which do not vanish at all zero dimensional cusps. If such a form is an eigenform of some power T(p)m, m > 1, of the Hecke operator T(p) with respect to at least one prime p = +__1 mod q and if the weight o f f is big enough, r > n + 1, then this form is uniquely determined by the values of f at the z...
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(m,n)6=(0,0) y |mz+n|2s is the nonholomorphic Eisenstein series on the upper half plane, then for all y sufficiently large, E(z, s) has a ”Siegel zero.” That is E(z, β) = 0 for a real number β just to the left of one. We give a generalization of this result to Eisenstein series formed with real valued automorphic forms on a finite central covering of the adele points of a connected reductive al...
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Let F ∈ Sk(Sp(4,Z)) be a cuspidal Hecke eigenform of degree 2. Let μ(n), n > 0, be the Hecke eigenvalues. It is known that F is in the Maaß space (i.e., F is a Saito-Kurokawa lifting), if and only if μ(n) > 0 for all n; see [2]. On the other hand, Kohnen has recently proved (see [6]) that if F is not in the Maaß space, then the sequence μ(n), n > 0, has infinitely many sign changes. The proof m...
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ژورنال
عنوان ژورنال: International Journal of Number Theory
سال: 2017
ISSN: 1793-0421,1793-7310
DOI: 10.1142/s179304211750021x