Jacobi Forms and Discrete Series Representations of the Jacobi Group.
Jacobi forms on symmetric domains and torus bundles over Abelian schemes.
Jacobi forms over imaginary quadratic number fields
Jacobi-Eisenstein series and -adic interpolation of symmetric squares of cusp forms
The aim of this paper is to construct and calculate generating functions connected with special values of symmetric squares of modular forms. The Main Theorem establishes these generating functions to be Jacobi-Eisenstein series i.e. Eisenstein series among Jacobi forms. A theorem on -adic interpolation of the special values of the symmetric square of a -ordinary modular form is proved as a corollary of our Main Theorem.
Jacobi-Eisenstein series of degree two over Cayley numbers.
We shall develop the general theory of Jacobi forms of degree two over Cayley numbers and then construct a family of Jacobi- Eisenstein series which forms the orthogonal complement of the vector space of Jacobi cusp forms of degree two over Cayley numbers. The construction is based on a group representation arising from the transformation formula of a set of theta series.
Jacobiformen und Thetareihen.
K-finite Whittaker functions are of finite order one
We prove a finite order one type estimate for the Whittaker function attached to a K-finite section of a principle series representation of a real or complex Chevalley group. Effective computations are made using convexity in ℂⁿ, following the original paper of Jacquet. As an application, we give a simplified proof of the known result of the boundedness in vertical strips of certain automorphic L-functions, using a result of Müller.
Kida's formula and congruences.
Kloosterman identities over a quadratic extension II
Kloosterman integrals and base change for GL (2).
Kloosterman Sums and Fourier Coefficients of Cusp Forms.
Kloosterman sums for Clifford algebras and a lower bound for the positive eigenvalues of the Laplacian for congruence subgroups acting on hyperbolic spaces.
Kloosterman sums in residue classes
We prove upper bounds for sums of Kloosterman sums against general arithmetic weight functions. In particular, we obtain power cancellation in sums of Kloosterman sums over arithmetic progressions, which is of square-root strength in any fixed primitive congruence class up to bounds towards the Ramanujan conjecture.
Kloosterman-Fourier inversion for symmetric matrices
We formulate a Kloosterman transform on the space of generalized Kloosterman integrals on symmetric matrices, and obtain an inversion formula. The formula is a step towards a fundamental lemma of the Jacquet type. At the same time it hints towards a conjectural relative trace formula identity, associated with the metaplectic correspondence.
Koecher-Maass series of a certain half-integral weight modular form related to the Duke-Imamoḡlu-Ikeda lift
Let k and n be positive even integers. For a cuspidal Hecke eigenform h in the Kohnen plus space of weight k - n/2 + 1/2 for Γ₀(4), let f be the corresponding primitive form of weight 2k-n for SL₂(ℤ) under the Shimura correspondence, and Iₙ(h) the Duke-Imamoḡlu-Ikeda lift of h to the space of cusp forms of weight k for Spₙ(ℤ). Moreover, let be the first Fourier-Jacobi coefficient of Iₙ(h), and be the cusp form in the generalized Kohnen plus space of weight k - 1/2 corresponding to under the...
Koecher-Maaß-Series for Modular Forms of Quaternions.
Kolyvagin's method for Chow groups of Kuga-Sato varieties.
Kompaktifizierung des Humbertschen Fundamentalbereichs.
Konstruktion von Spitzenformen beliebigen Grades mit Hilfe von Thetareihen.
Konstruktionsprinzipien für Untergruppen der Modulgruppen mit einer oder zwei Spitzenklassen.