Search for dissertations about: "eisenstein series"

Showing result 1 - 5 of 11 swedish dissertations containing the words eisenstein series.

  2. 1. Vector-valued Eisenstein series of congruence types and their products

    Author : Jiacheng Xia; Chalmers tekniska högskola; []
    Keywords : NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; Hecke operator; Fourier expansion of modular forms; congruence type; products of Eisenstein series; vector-valued modular forms;

    Abstract : Historically, Kohnen and Zagier connected modular forms with period polynomials, and as a consequence of this association concluded that the products of at most two Eisenstein series span all spaces of classical modular forms of level 1. Later Borisov and Gunnells among other authors extended the result to higher levels. READ MORE

  4. 2. Some Cases of Kudla’s Modularity Conjecture for Unitary Shimura Varieties

    Author : Jiacheng Xia; Chalmers tekniska högskola; []
    Keywords : NATURVETENSKAP; NATURAL SCIENCES; special cycles; Eisenstein series; spherical designs; central L-values; unitary Shimura varieties; Jacobi forms; rational points; generating functions; the circle method; Kudla s modularity conjecture; theta series; Rankin--Selberg method;

    Abstract : A common theme of the thesis is the interplay of symmetry and rigidity, which is a general phenomenon in mathematics. Symmetry is a notion related to the degree to which an object remains unchanged under transformations, and rigidity is a notion that in terms of physics can be thought of as a lack of freedom, which leads to stronger properties of an object than we normally expect. READ MORE

  5. 3. Computing Vector-valued Modular Forms of Congruence Types and of Some Extension Types

    Author : Tobias Magnusson; Chalmers tekniska högskola; []
    Keywords : NATURVETENSKAP; NATURAL SCIENCES; eisenstein series; modular forms; iterated eichler-shimura integrals; vector-valued modular forms;

    Abstract : This thesis explores applications of vector-valued modular forms of congruence and extension types to scalar-valued modular forms for congruence subgroups with a character, higher order modular forms, and iterated Eichler-Shimura integrals of depth one and two, including considerable generalizations thereof. In \textsc{Paper I} (co-authored with Martin Raum), we present an algorithm for computing bases for spaces of vector-valued modular forms of congruence type and of weight at least $2$ in terms of products of components of vector-valued Eisenstein series. READ MORE

  6. 4. Some applications of representation theory in homogeneous dynamics and automorphic functions

    Author : Samuel Charles Edwards; Andreas Strömbergsson; Henrik Schlichtkrull; Uppsala universitet; []
    Keywords : NATURVETENSKAP; NATURAL SCIENCES; automorphic functions; effective equidistribution; Eisenstein series; homogeneous dynamics; horospheres; lattices; Lie groups; representation theory; Mathematics; Matematik;

    Abstract : This thesis consists of an introduction and five papers in the general area of dynamics and functions on homogeneous spaces. A common feature is that representation theory plays a key role in all articles. READ MORE

  7. 5. Automorphic forms and string theory: Small automorphic representations and non-perturbative effects

    Author : Henrik Gustafsson; Chalmers tekniska högskola; []
    Keywords : NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; instantons; automorphic forms; automorphic representations; Eisenstein series; U-duality; non-perturbative effects; string theory;

    Abstract : This compilation thesis stems from a project with the purpose of determining non-perturbative contributions to scattering amplitudes in string theory carrying important information about instantons, black hole quantum states and M-theory. The scattering amplitudes are functions on the moduli space invariant under the discrete U-duality group and this invariance is one of the defining properties of an automorphic form. READ MORE