#modular forms

[jadagul]

alexyar replied to your post: alexyar replied to your post: alexyar replied to...

“replace x with 1/y” so like…divide by x? :D

Replace, not divide.  So that your limit as x approaches infinity becomes a limit as y approaches zero.  I know how to do series expansions around zero.

(This is actually something that comes up in modular forms a lot, I think---you want the series expansion at infinity, so you write out the series in the variable q = 1/z).

[isomorphismes]

Alberto Verjovsky, Modular orbifold: arithmetic and dynamics

[isomorphismes]

the ring of classical modular forms is ℤ[E₄,E₆] ⊗ ℂ.

Frank Calegari, congruences between modular forms

[isomorphismes]

David Lowry Douda: Mistakes

[isomorphismes]

Abdelazz Nait Merzouk

Green is positive; red is negative. ℂ arguments can also be “in-between” (along 2 different paths, here shown as blue & yellow).

Felix Klein’s modular function ℑ: ℂP1 → ℂP1 equals

0 at the centers of the icosahedron's faces,

1 on the midpoints of its edges,

and ∞ at its vertices.

It satisfies all symmetries of the icosahedron: 

A₅’s generators are: aaa = bb = [ab]⁵ = leave alone. Enjoy.

— isomorphismes (@isomorphisms) May 17, 2018

via an exposition of the A-D-E structures by John Baez

made with:

fragmentarium http://syntopia.github.io/Fragmentarium/

shadertoy https://www.shadertoy.com 

[billloguidice]

Foundations of Computational Mathematics - The L-Functions and Modular Forms Database Project

Foundations of Computational Mathematics - The L-Functions and Modular Forms Database Project #mathematics #database #lfunctions #modularforms

From the journal, Foundations of Computational Mathematics, comes a paper on The L-Functions and Modular Forms Database Project. This paper is free to read (link) through September 2019.

Abstract

The Langlands Programme, formulated by Robert Langlands in the 1960s and since much developed and refined, is a web of interrelated theory and conjectures concerning many objects in number…

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[jadagul]

I don’t understand the second equality in your Frey curve? b^n is distinctly not c^n...

Hm, I think you’re right.  My source said the two curves were equivalent, but that doesn’t mean they’re actually the same curve; they just both work the same way and have similar properties.  I’ll edit that out since at the least it’s unimportant and confusing.  

[ebookspksite]

Free download Elliptic Curves, Modular Forms, And Their L-functions written by Other .