The first one we need to find a closed form solution to the integral of e^(x^2)dx. This I should be able to do myself (but obviously as I posted it, tips and help are welcome). Now this one, I just don't have time to solve myself, I was wondering if you could take a look at it for me.

It's called the Modularity theorem.

The theorem states that any elliptic curve over Q can be obtained via a rational map with integer coefficients from the classical modular curve,

Xₒ(N)

for some integer N; this is a curve with integer coefficients with an explicit definition. This mapping is called a modular parametrization of level N. If N is the smallest integer for which such a parametrization can be found (which by the modularity theorem itself is now known to be a number called the conductor), then the parametrization may be defined in terms of a mapping generated by a particular kind of modular form of weight two and level N, a normalized newform with integer q-expansion, followed if need be by an isogeny.

The modularity theorem implies a closely related analytic statement: to an elliptic curve E over Q we may attach a corresponding L-series. The L-series is a Dirichlet series, commonly written

∞ aᶰ

L(s, E) = Σ

ᶰ=1 nᶳ

The generating function of the coeffcients Aᶰ is then

∞

f(q, E) = Σ aᶰqᶰ

ᶰ=1

If we make the substitution

q=e ²piᵢᵗ

we see that we have written the Fourier expansion of a function f(ᵗ, E) of the complex variable τ, so the coefficients of the q-series are also thought of as the Fourier coefficients of f. The function obtained in this way is, remarkably, a cusp form of weight two and level N and is also an eigenform (an eigenvector of all Hecke operators); this is the Hasse–Weil conjecture, which follows from the modularity theorem.

Some modular forms of weight two, in turn, correspond to holomorphic differentials for an elliptic curve. The Jacobian of the modular curve can (up to isogeny) be written as a product of irreducible Abelian varieties, corresponding to Hecke eigenforms of weight 2. The 1-dimensional factors are elliptic curves (there can also be higher dimensional factors, so not all Hecke eigenforms correspond to rational elliptic curves). The curve obtained by finding the corresponding cusp form, and then constructing a curve from it, is isogenous to the original curve (but not, in general, isomorphic to it).

looking forward to your answer

serz xoxo

Just googling that has given me a headache.

24/03/2012 00:36Posted by MisswenchJust googling that has given me a headache.

Dear Xoo, I am sad to hear that you feel your hat does not have much sex appeal. However, I have done some research for you and can offer you some alternatives, while keeping your original flair intact.

Clever Hat: http://www.wowhead.com/item=18308

Stylin' Purple Hat: http://www.wowhead.com/item=25680

Ranger Hat: http://www.wowhead.com/item=24745

Perhaps you consider one of these to be more 'swagging' or give 'better flow'? Good luck and I hope you find the hat of your dreams.

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Hello Scrumpyjack, first I feel I must congratulate you on such a great name! that particular brand of Cider is a wonderful tipple on a warm summer's evening. Now, onto your question.

Although I do not condone violence of any kind, I feel that in this case it may be, dare I say it, the best option. Your class is known for its ruthlessness and pure hatred of all that is good in the world. So I offer you the following advice. TEAR THEM LIMB FROM LIMB AND NEVER LET THEM FORGET IT. SCAR THEM IN PLACES THEY DIDN'T EVEN KNOW EXISTED. They will soon realise that a Mage would never be capable of such a thing.

Hope I helped and good luck!

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Hello Shikona, (or should I say Anna!) it is great to hear from you again. I am sorry to hear about your case of somewhat mistaken identity. This is a tricky one but I believe I have found an answer of sorts. First you must find a role in your raid team/guild that you want to fill. You must then, however possible (trade chat perhaps, although recruitment forums could also work) find a girl called Amanda.

When you raid with your new friend Amanda, when her name is called you too must also reply. Your raid will become furious at the confusion it is causing!. They will then ask you to come up with another name to be known as, at which point you suggest your correct name, Anna.

And voila, you have your name back again. In regards to the wrong age issue, simply wait until your next birthday. Then it will be correct.

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Hello Serze, it is also nice to see you back on the thread, searching for more fulfillment.

I am afraid that your requests today are difficult - not because of my lack of knowledge but rather, due to the mathematical constraints of the equations you have posted.

In regards to e^(x^2)dx, the integral simply cannot be found. The e^(x^2) functions are of a class where the antiderivatives are defined as transcendental, and so are not expressed in terms of a normal function. So it is regrettable that it is simply impossible to answer, unfortunately. To further your reading and understanding however, I would suggest (or advise, rather) to research the differential galois theory.

In regards to the Modularity Theorem, I'm not quite sure what you want answering here. The equations you posted are a statement that has already been answered, and thus there is nothing to answer.

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I hope everyone has expanded the reaches of their knowledge and their understanding of the physical and spiritual realm around us, and remember, I'm always here to help.

Kind regards,

Oi

This is my first step into history, please oi help me fullfil my dreams.

I fully support your goal to disprove and invalidate the theorem in question. The world of science is made up of theories, many of which work on paper but in the real world fail to materialise. But then, who's to say what is and isn't real? are we real or are we merely figments of some twisted individual's imagination.

The only real reality is what exists in our hearts, and that we know for certain.

A not so wise man once asked me, "Oi, prove to me the soul exists". So I responded, "No, you.".

He wasn't ready.

Anyway, please do let me know if you make any progress disproving his theorem, although as it's a theorem, I suspect it's not been proven anyway.

I guess we won.

Kind regards,

Oi

If humans can grow up to 8 feet, why have I never seen anyone with more than 2?

Don't mind me. I'm a ninja.

Don't mind me. I'm a ninja.

WHO SAID THAT?!

Hello Shikona, it's great to hear from you again. I hate to embarrass you in this way but I think you have become slightly confused! I think that factoid of yours refers to the height of humans rather than the anatomical structure.

I think when you read this and realise the mix up we'll all have a jolly good laugh about it!

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I thought there would be more wisdow to provide but alas there is not. I thought I heard someone say something but when I looked around there was no-one there. I guess Akassá heard the same as me. The wind perhaps.

(Hehe! aren't we a silly lot.)

Kind regards, and I hope to hear from more of you soon,

Oi

The sun is shining, the flowers are in bloom and the animals bask in the rays of light. It truly is a wonderful day and we're blessed to exist in this time and place.

Anyway, on to your question. I am afraid that filling up the bath with a shower will use the same amount of water and thus it will not make any difference.

I must commend you however on your thoughtfulness towards water preservation.

Hope this helped and kind regards,

Oi

Call me zelda one more god damn time

If jellyfish are 99% water. If I inject 1% of water into it. Will it turn into water?

My continued quest for world domination/world peace/the end of hunger/bashing some noobs has so far produces very little results. Any ideas on what I can improve upon?

With regards,

Anarien

(lol@Amanda)

I too have a question for your logic eng...brain. What is the root of -1? Another would be, consider that Pinnochio said, "My nose is about to grow". First we think, ah he's telling the truth so his nose will not grow but then, the mystery unravels further, he has inadvertently told a lie at the same time as his nose will not grow but he is still telling the truth. What will happen? And should i take precautionary steps to stop Pinniochio from uttering these words to stop a tear in the time-space-fish pie-continium?

Kind regards,

Bear-O-Dactyl.

Edit: yes, i'm a cow. deal with it.

And don't you dare quote Karl Pilkington and try to pass it off as something you said!

Anyway, I will hope I can help in any way I can, so on the questions.

Hello Serze, it's nice that our paths meet once again. I am not quite sure what to make of this statement, because if I recall correctly (my knowledge is actually vast and infinite and so is my memory - but anyway) I have no yet called you Zelda. However, if this is a request to me then I shall fulfil your wishes: Hello Zelda, lovely to meet you!

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Hello Shikona, I am so glad that I have been able to expand your mind and understanding of the world. There is no limit to what our brain can achieve, it is as vast and unexplored as the universe we live in.

Now, in regards to your question, it is an interesting one and I hope I can succinctly provide an answer. First, although you are close in your facts, Jellyfish are closer to 5% of organic matter rather than 1%. Also, I don't want to be 'party pooper' but given how fragile Jellyfish are, removing it from water to inject it with 1% more water would cause the structure to totally collapse. Also, it would seem likely that it would only lose more water being outside the water, infact increasing the jelly to water ratio.

BUT, let's assume this was actually possible, no, the Jellyfish would still exist. The organic matter 1% of the Jellyfish (even if you lowered that percentage) would not disappear.

Hope this helped!

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Hello Anarien, it's great to meet you.

I can first see a very obvious major flaw in your aims which would cause your mission to become very inefficient. First, it is not clear what it is. You strive for 'World Domination' but then 'World Peace'. Although it's not totally impossible to achieve this via being a nice fellow, surely 'Bashing Noobs' is an oxymoron of 'Peace'.

My advice to you would be to choose one goal and then fully commit to it. Being the sentinent, tranquil being I am, I would very much strive for World Peace, or perhaps the abolishment of Hunger. However, given that you listed World Domination first, perhaps this is your primary goal. To achieve this I would recommend giving out Haribo to everyone you know, and to all those you meet. It is far easier to get to the top of the good chain and be an Alpha kind of person via trust and love.

Good luck with your goal and may the wind blow into your sails of life.

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Hello Jooba/Bear/Cow, thanks for the questions.

In normal mathematic conventions, there is no root of -1. However, some mathematicians (past students of mine, actually), decided to assume that the root did exist, and named it 'i', for 'imaginary'. Hope this was the kind of answer you were looking for.

In regards to your second question, first, thanks for looking out for Pinocchio. A lot of people (wrongly) assume he is a fictional character but this is the kind of negativity and prejudice he ends up facing far too often.

Anyway, in regards to the question. The answer is actually rather simple and luckily unlikely to cause him any harm. As he has told neither a lie, nor the truth (via a paradox) his nose will stay as it normally is. Phew!

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Hello Handeath, nice to see you.

Although there was no question in your post, I feel the need to chip in. IQ is an interesting, but I feel, flawed measurement of a human's intelligence. What I feel we really need to measure is our spiritual breadth, the integrity of our soul and the measure of our very essence.

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I hope these answers all helped and I hope the sun is shining favourably upon you all, be it in your physical or spectral forms.

Kind regards,

Oi

Could you explain in exact detail how on earth gnomes and goblins are born?

It is an incredibly irritating thought to try and decipher... and also why do male blood elves look like they have had that balls kicked in when they stand?