Rational functions and Modular forms
Rational functions and Modular forms - Mathematisches Institut
One of them uses automorphic Poincare series and the other one theta functions. We start a third elementary approach to modular forms using rational functions ...
Rational functions and modular forms
Weil's converse theorem, Eisenstein series, rational functions, contour integration. c. 2020 American Mathematical Society. 4151. Licensed to ...
Modular Functions and Modular Forms
... modular functions for Γ0(N) as its field of rational functions. Now write FN (X, Y ) for the polynomial constructed in Theorem 6.1, and let C be the curve ...
"Modular function" redirects here. A distinct use of this term appears in relation to Haar measure. ... , that roughly satisfies a functional equation with ...
Modular forms with rational and $p$-integer coefficients (mod $p$)
Let f∈Z(p)[[q]] the q-expansion of a modular form of weight w>14, and write f=∑a,bca,bEa4Eb6, and we want to show that the ca,b are p-integers.
Rational functions and modular forms | Request PDF - ResearchGate
Request PDF | On Jun 30, 2020, J. Franke published Rational functions and modular forms | Find, read and cite all the research you need on ResearchGate.
CHAPTER 9 - Modular Forms with Rational - Periods
The appearance of interesting functions as Fourier coefficients, coupled with the finite dimensionality of the spaces of modular forms, leads to non-trivial.
Naive construction of modular forms of rational weights - MathOverflow
You could simply choose the fourth root that makes the transformation law work for your function, so you would be setting up the definitions so ...
Modular Forms Lecture 2: elliptic functions | LARRY ROLEN
modular forms due to their connection to elliptic functions. In turn, this ... nomial is a holomorhpic function, and any rational function is a meromorphic.
Modular forms: Modular functions - YouTube
We classify all meromorphic modular functions, showing that they are all rational functions of the elliptic modular function j. As an ...
25 Modular forms and L-functions - MIT Mathematics
removed the (necessarily rational) singular point, so we reduce ap by one. ... 25.8 L-functions of elliptic curves versus L-functions of modular ...
Rational points on ellipsoids and modular forms - arXiv
The theory of modular forms and spherical harmonic analysis are applied to establish new best bounds towards the counting and equidistribution of rational ...
MODULAR FUNCTIONS AND ELLIPTIC CURVES
MODULAR FORMS LECTURE 13: MODULAR FUNCTIONS AND. ELLIPTIC CURVES. LARRY ROLEN ... = C(j), i.e., modular functions are rational functions in j. 1. Page 2. 2.
Rational points on modular elliptic curves Henri Darmon
p-adic L-functions and p-adic periods of modular forms. Invent. Math. 111 (1993), no. 2, 407–447. [GZ84]. B.H. Gross and D.B. Zagier. Heegner points and ...
Modular Function -- from Wolfram MathWorld
... form f(tau)=sum_(n=-m)^inftya(n)e^(2piintau) (Apostol 1997, p. 34). Every rational function of Klein's absolute invariant J is a modular function, and every ...
By origin ; Dirichlet character · Classical modular form · Elliptic curve over Q \mathbb{Q} Q ; Hilbert modular form · Bianchi modular form · Elliptic curve over ...
Newforms with Rational Coefficients
These modular forms are functions on the upper half plane {z ∈ C : Im(z) > 0} satisfying certain transformation laws which become less demanding as N becomes ...
Elliptic Modular Forms and Their Applications
functions and modular forms as in some sense the analogues of rational num- bers and integers, respectively. From the point of view of functions on lattices,.
Finite Modular Forms - ScienceDirect.com
upper half-plane ). " . Therefore, a meaningful theory of "nite modular forms may be developed, i.e., of rational functions on )/K with the familiar.
LMFDB - The L-functions and modular forms database
Welcome to the LMFDB, the database of L-functions, modular forms, and related objects. These pages are intended to be a modern handbook including tables, ...