then one might consider the Dirichlet series $\displaystyle \sum \frac{1}{I_1(q)^{s_1}I_2(q)^{s_2}}$, where $I_1$ and $I_2$ are the two generators of the invariants (there is a cannonical choice), and where we sum over equivalence classes of quadratic forms
but he did it just over the discriminant. My advisor's thing is multiple Dirichlet series, so we're all about more complex variables
the idea is that with more invariants, we should have more information. If we understood poles, residues, and analytic continuations, we'd be golden in many ways
well, it turns out that binary n-ic forms (not just quadratic or cubic), analyzed in this way, can always be written as sums of zeta functions and L-functions, which are lovely amazing things that everyone wants to understand. And I played with that
since then, I've gone even more analytic. There's representation theory and algebra in that, but now I look more at moments of L-functions in critical strips, subconvexity bounds, working on Lindelhof-hypothesis type stuff
@AlexYoucis ah that's fascinating. i really like the methods, but I often don't care about the results
I just managed to show that a particular set of coefficients has infinitely many sign changes. Really beautiful theory, clear flow of ideas. Amazing cancellation. But really, who cares about these sign changes?
@mixedmath Well, math wouldn't be a beautiful mosaic if we didn't have different tastes :) My dislike is most likely really just a function of ignorance.
@mixedmath It's actually predominantly a girl's name, from what I'm led to believe. And yes, the Qiaochu Yuan who participates on stacexchange is at Berkeley.
@mixedmath I met a guy recently from Brown. Dan Miller?
@AlexYoucis any level. Most of the current stuff is at low-mid undergraduate. Will Jagy has a post in the process that's research-math, some new stuff. I'll put some research math there sometime (though I have a post in the works that's popmath, essentially)
the rule should be: if it would be of interest to the MSE community, it's reasonable written, and it's not offensive - then it's fair game for the blog
@AlexYoucis that's a good question. I dunno - I'd have to see the post. If you're anything like me, the intended audience will become more coherent once you sit down and start writing
(if you're more responsible than I am, then I suppose you might decide beforehand what your audience knows and doesn't know, and then pitch it appropriately)
@m1cky22 yep. But that's not really a good reason to double in math. I think that perhaps you should double in math if it's something that you want to do, or that you think will benefit you.
and for what it's worth, if you intend on becoming a physicist, I would recommend learning a good amount of math
Oh I should have clarified. I actually love math, I was thinking of going purely into math but I wasn't sure what I can do with math besides teach. I'm currently self-studying Algebra (I started using D&F) and I love it. What can I do with a math degree though?
Hi, could someone give me a hand? I would really like to resolve this tonight and it is too late to ask anyone I know. I am trying to properly cite the following source: http://waset.org/Publications/integer-complexity-breaking-the-θ-n2-barrier/6770
Using the bibtex code. However, I am using the plain bibliography style that does not include the publisher and I am concerned that my citation will be considered poorly written because of that. Is this going to be okay? I looked online to see how others are citing the article, but I don't think it helps me.
@robjohn For example, one of the citations looks like this, up to some formatting lost:
"K. Mahler and J. Popken, On a maximum problem in arithmetic. (Dutch), Nieuw Arch. Wiskunde"
Everything follows a name, title, journal, volume, issue, page format, but the bibtex entry given from the source I linked does not include a journal, but a publisher instead. In the plain bibliography style publishers are omitted so the citation just goes author, title, volume, issue, page. I am concerned that it looks like a glaring mistake in the bibliography.
Having added to it yet again, I'm concerned that this question of mine is too long: http://math.stackexchange.com/questions/873429/a-reflective-subcategory-of-the-category-of-inverse-semigroups. Would it be worth posting a question on the meta site about it?
I'm aware that there are similar questions on there . . .
In the case of the absolute value function, the limit at the point zero from the left and the right give 1 and -1 respectively, the derivative you are wrote is already assuming existence.
@VibhavPant As far as I am concerned, it is not terribly important whether an author classifies points where the derivative is not defined, or even end points as critical points or not. You should be keeping in mind that they must be in the domain of $f$ more than anything. There is no point in classifying a point as a candidate for maxima/minima if it isn't in the domain of the thing you are trying to optimize to begin with.
@BalarkaSen I will not tell you where I heard this to not emabarrass the person who said it, but it was in a question session after a number theory lecture when a person in the audience asked: "Would you be interested in proving the Goldbar conjecture?"
Maybe it is not a true story, but that is what my ears heard.
@Khallil well, somebody asked whether there might be some connection of RH with Collatz and I gave a rough connection in between them, but i am not happy about my argument. i am trying to see if there's any other argument.
@Hakim How so? Is it that I cancelled off the $sin(h)$ terms after expanding the numerator with the double angle formula?
I think it might be justified as the limit looks at the value the function approaches and specifically not the value at the point, which is $0$ in this case.
@Khallil or simply $$\require{cancel}\lim_{h\to0}{\left[\cancelto{\ln(1/\sqrt2)}{\ln\left(\sin(h+\tfrac\pi4)\right)}-\cancelto{-\infty}{\ln\left(\sin h\right)}\right]}.$$
I've seen the dub twice and the sub a few more times! Danzo vs Sasuke is another one of my favourites. Pain vs Naruto is of course, one of the greatest!
Wait, I found her backstory. It is just as deep as Naruto and Sasukes.
During her early years in the Academy, Sakura was frequently bullied by others due to her large forehead. To try and combat this, Sakura used her fringe to hide her forehead, fuelling the other kids' teasing by indicating she was sensitive about it. Ino Yamanaka, realising this, helped Sakura by giving her a red ribbon that she used as a way of drawing attention to the cuter features of her forehead, which helped Sakura overcome her insecurity.
@ThomasAndrews From one of his publications he tries to prove: "à partir de 11, tous les nombres premiers se terminent par 1, 3, 7 ou 9." which translates to "from 11, every prime numbers ends with 1, 3, 7 and 9"
@ThomasAndrews He also seems to be making up conspiracy theories, quoting him: "*Si maintenant ce site est infesté de franc-ma-cons *" translates to "if now this site is infested with freemasons.." lol
@ThomasAndrews come on you understand everything. The real true is that the other part of the solution includes some confidential military and industrial techniques. — Thierno M. SOW32 mins ago
if the user who started the bounty (not the OP) has answered the question first and has maximum number of upvotes on his answer .. will the bounty be awarded to his answer ?!
Yeah, that would be unfair, because you could offer a bounty, lots of people could then answer your question, and then you'd essentially be able to "revoke" the offered bounty.
@DanielFischer ic .. and if I was the second to answer (with 2 upvotes), and I edited my answer after a 3rd answer was added .. then who gets 1/2 bounty amount (assuming the one who puts the bounty doesn't award it manually before the grace period ) ?!
@r9m If the bounty is not manually awarded, a) if the bounty was by the asker, and (s)he accepted an answer during the bounty period [I don't know whether that answer must have been posted during the bounty period, or if that case also applies for answers posted previously], that gets the full bounty awarded by the system. Otherwise, the system only awards half the bounty, to the highest scoring answer posted during the bounty period, provided that answer has a score of at least 2.
I don't know what happens in case of a tie. Look on meta (meta.stackexchange.com), "How do bounties work" or something similar.
