Siegfried Böcherer
University of Mannheim
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Featured researches published by Siegfried Böcherer.
Nagoya Mathematical Journal | 1991
Siegfried Böcherer; Rainer Schulze-Pillot
The two main problems in the theory of the theta correspondence or lifting (between automorphic forms on some adelic orthogonal group and on some adelic symplectic or metaplectic group) are the characterization of kernel and image of this correspondence. Both problems tend to be particularly difficult if the two groups are approximately the same size.
Manuscripta Mathematica | 1984
Siegfried Böcherer
It is well known that the Fourier coefficients ank(T) of Siegels Eisenstein series of degree n and weight k are rational numbers with bounded denominators [14], [15]. In this paper we introduce a number bnk(T), which is equal to ank(T) in many cases. This number can be computed in an elementary way. From our explicit formulas for bnk(T) we can easily get results about the denominators of the Fourier coefficients ank(T), which are better than those obtained by Siegel in his difficult paper [15].
Communications in Mathematical Physics | 2003
Siegfried Böcherer; Peter Sarnak; Rainer Schulze-Pillot
Motivated by problems of mathematical physics (quantum chaos) questions of equidistribution of eigenfunctions of the Laplace operator on a Riemannian manifold have been studied by several authors. We consider here, in analogy with arithmetic hyperbolic surfaces, orthonormal bases of eigenfunctions of the Laplace operator on the two dimensional unit sphere which are also eigenfunctions of an algebra of Hecke operators which act on these spherical harmonics. We formulate an analogue of the equidistribution of mass conjecture for these eigenfunctions as well as of the conjecture that their moments tend to moments of the Gaussian as the eigenvalue increases. For such orthonormal bases we show that these conjectures are related to the analytic properties of degree eight arithmetic L-functions associated to triples of eigenfunctions. Moreover we establish the conjecture for the third moments and give a conditional (on standard analytic conjectures about these arithmetic L-functions) proof of the equidistribution of mass conjecture.
Forum Mathematicum | 2016
Siegfried Böcherer; Toshiyuki Kikuta
Abstract We show that a Siegel modular form with integral Fourier coefficients in a number field K, for which all but finitely many coefficients (up to equivalence) are divisible by a prime ideal 𝔭
arXiv: Number Theory | 2014
Siegfried Böcherer; Shoyu Nagaoka
{\mathfrak{p}}
arXiv: Number Theory | 2001
Siegfried Böcherer; Masaaki Furusawa; Rainer Schulze-Pillot
of K, is a constant modulo 𝔭
Abhandlungen Aus Dem Mathematischen Seminar Der Universitat Hamburg | 1990
Siegfried Böcherer
{\mathfrak{p}}
Manuscripta Mathematica | 2018
Siegfried Böcherer; Hirotaka Kodama; Shoyu Nagaoka
. Moreover, we define a notion of mod 𝔭
Advances in Mathematics | 2018
Siegfried Böcherer; Soumya Das
{\mathfrak{p}}
Mathematische Zeitschrift | 1983
Siegfried Böcherer
singular modular form and discuss a relation between its weight and the corresponding prime p. We discuss some examples of mod 𝔭