Sökning: "modular form"

Visar resultat 1 - 5 av 52 avhandlingar innehållade orden modular form.

1. 1. Admissible covers, modular operads and modular forms

   Författare :Dan Petersen; Carel Faber; Alessandro Chiodo; KTH; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES;

   Sammanfattning : This thesis contains three articles related to operads and moduli spaces of admissible covers of curves. In Paper A we isolate cohomology classes coming from modular forms inside a certain space of admissible covers, thereby showing that this moduli space can be used as a substitute for a Kuga–Sato variety. LÄS MER

3. 2. Modular Normalization with Types

   Författare :Nachiappan Valliappan; Chalmers tekniska högskola; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Programming Languages; Functional Programming;

   Sammanfattning : With the increasing use of software in today’s digital world, software is becoming more and more complex and the cost of developing and maintaining software has skyrocketed. It has become pressing to develop software using effective tools that reduce this cost. LÄS MER

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

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

   Sammanfattning : 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. LÄS MER

5. 4. The density of rational points and invariants of genus one curves

   Författare :Manh Hung Tran; Chalmers tekniska högskola; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; genus one; discriminant; modular form; Elliptic curve; height; descent; determinantal representation; invariant; rational point; theta function.; determinant method;

   Sammanfattning : The present thesis contains three papers dealing with two arithmetic problems on curves of genus one, which are closely related to elliptic curves. The first problem is to study the density of rational points presented in Papers I and II. LÄS MER

7. 5. Summation formulae and zeta functions

   Författare :Johan Andersson; Mikael Passare; Aleksandar Ivic; Stockholms universitet; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; zeta function; summation formula; automorphic form; modular group; Kloosterman sum; Selberg theory; power sum method; MATHEMATICS; MATEMATIK;

   Sammanfattning : This thesis in analytic number theory consists of 3 parts and 13 individual papers.In the first part we prove some results in Turán power sum theory. We solve a problem of Paul Erdös and disprove conjectures of Paul Turán and K. Ramachandra that would have implied important results on the Riemann zeta function. LÄS MER