User talk:Jakob.scholbach/Archives/2012/September

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The Signpost: 03 September 2012

The Signpost: 10 September 2012

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The Signpost: 17 September 2012

Modular Forms edit of 2 July 2011

Hi Jacob,

I was wondering about two Wikipedia edits about Math topics, one of them was done by yourself, and one I haven't remembered details of (but could be found).

The definition of modular forms as functions on lattices seemed quite clear and simple, and I am not sure if I'm looking at the revision history correctly, it seems it may have been deleted by you (you can correct me if this is wrong).

The general question in my mind is whether Wikipedia articles are like shifting sands, where over time they degenerate to what is popular. Also there may be a political view that modular forms should be conceptualized in one or another particular way that leads on to various generalizations...and sadly, or perhaps inevitably, this is how Maths proceeds into the future. The particular language that is used to state a small theorem is carried over to more general settings, and whereas in the particular case the languaged used does not matter, it affects what the generalization should be.

The definition of a function Lattices in C -> Complex numbers which satisfies that when a lattice is expanded by a complex number c the function is multiplied by c^k, seems like an uncomplicated definition. The fact that the function is analytic with respect to varying one or another basis element of the lattice makes sense too, if one wants to talk about analytic modular forms (it would presumably make sense to remove this and talk about continuous or even discrete modular forms but by convention when people talk about modular forms they are using complex analysis). The condition that the function is bounded if the lattice avoids a neighbourhood of 0 may correspond to the strange third condition 'meromorphic at the cusp' though I'm not sure. Getting a sensible definition shouldn't be disallowed as 'original research' -- it is in some sense going backwards, getting rid of nonsense and tendentious research that gets attached to definitions (such as here the tendentious relation with group theory and with SL_2).

I admit that I have not thought yet about whether that third condition about boundedness makes sense or not so I'm not here trying to impress you or anything, but I am wondering what was the context in which the section was deleted.

Analogously, there used to be a really nice section about Feynman diagrams, which got deleted and overwritten by some advanced statistics having to do with Ito's lemma. I am thinking that it is pretty clear when a definition is uncomplicated -- depends on a minimum of machinery.

If I were to be cynical I'd say that the deletion of the 'functions on lattices' section of the modular forms article was done by people with an interest in saying, you can't understand this unless you already know Lie groups and arithmetic groups and that it leads on necessarily to Langlands theory.

And I'd say that the Feymnan diagram article was taken over by people who are saying you first have to understand stochastic processes etc.

Where possible, definitions should be simple and easy things that don't require expert specialist knowledge. What do you think of this notion...is it the right notion, and also is there any prospect of restoring the Feyman diagram description and the modular forms description to their earlier naive forms?

thx

Thanks for your message. The article still states quite clearly "A modular form can equivalently be defined as a function F from the set of lattices Λ in C (that is, subgroups of C that are isomorphic to Z2) to the set of complex numbers which satisfies certain conditions: ...". Therefore, the simple definition you are looking for is just there. Jakob.scholbach (talk) 15:44, 23 September 2012 (UTC)


Yes, that explains the reason for its deletion: there is no deletion!

Happy now. Obviously you can disregard my wrong comment about the modular forms article. Maybe I'd better re-read Feynman diagrams, the other article which I mentioned even more vaguely and see if I made the same mistake!

Createangelos (talk) 03:18, 24 September 2012 (UTC)

The Signpost: 24 September 2012

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