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Dive into the research topics where Siegfried Böcherer is active.

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Featured researches published by Siegfried Böcherer.


Nagoya Mathematical Journal | 1991

Siegel modular forms and theta series attached to quaternion algebras

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

Über die Fourierkoeffizienten der Siegelschen Eisensteinreihen

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

Arithmetic and Equidistribution of Measures on the Sphere

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

On mod p singular modular forms

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

On p-Adic Properties of Siegel Modular Forms

Siegfried Böcherer; Shoyu Nagaoka

{\mathfrak{p}}


arXiv: Number Theory | 2001

On the global Gross-Prased conjecture for Yoshida liftings

Siegfried Böcherer; Masaaki Furusawa; Rainer Schulze-Pillot

of K, is a constant modulo 𝔭


Abhandlungen Aus Dem Mathematischen Seminar Der Universitat Hamburg | 1990

Über den Kern der Thetaliftung

Siegfried Böcherer

{\mathfrak{p}}


Manuscripta Mathematica | 2018

On the kernel of the theta operator mod p

Siegfried Böcherer; Hirotaka Kodama; Shoyu Nagaoka

. Moreover, we define a notion of mod 𝔭


Advances in Mathematics | 2018

Petersson norms of not necessarily cuspidal Jacobi modular forms and applications

Siegfried Böcherer; Soumya Das

{\mathfrak{p}}


Mathematische Zeitschrift | 1983

Über die Fourier-Jacobi-Entwicklung Siegelscher Eisensteinreihen II

Siegfried Böcherer

singular modular form and discuss a relation between its weight and the corresponding prime p. We discuss some examples of mod 𝔭

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Soumya Das

Tata Institute of Fundamental Research

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Bernhard Heim

German University of Technology in Oman

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Toshiyuki Kikuta

Fukuoka Institute of Technology

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Jan Hendrik Bruinier

Technische Universität Darmstadt

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