Проблема Бибербаха

Репутация которого запятнана связями с нацистами) уходит корнями в значительно более раннее утверждение, высказанное в 1851 г. Бернхардом Рима- ном. Теорема Римана — одно из первых утверждений, связывающих анализ и теорию функций с топологией — наукой, представляющей собой обобщение определенных аспектов геометрии. Чтобы понять теорему Римана, нужно рассмотреть на плоскости произвольную односвязную область, т.е. область, устроенную сколь угодно сложно, но не имеющую «дыр». Риман, апеллируя к физическим соображениям, доказал, что для любой такой области обязана существовать «хорошая» функция, отображающая круг единичного радиуса на эту область, и притом так, чтобы каждой точке области отвечала одна и только одна точка внутри круга (строгое доказательство его теоремы было получено в начале нашего века).

Функции, отображающие одну область плоскости в другую, удобнее всего представлять с помощью комплексных чисел. В математическом отношении с такими функциями обычно легче иметь дело, если их можно записать в виде степенного ряда — суммы бесконечного числа членов. Например, функция ez, где z — комплексное число, может быть представлена в виде бесконечного ряда 1 + г + z2/2! + г3/3! + .

Предположение Бибербаха состояло в том, что есть определенная связь между условиями на данную функцию, фигурирующими в гипотезе Римана, и числовыми коэффициентами степенного ряда, представляющего эту функцию. Бнбербах рассмотрел первоначально одну специальную функцию комплексной переменной, исследованную математиком Паулем Кёбе. Это функция г/( 1 — z)2, где z также комплексное число. При отображении, осуществляемом функцией Кёбе, образы всех точек, лежащих внутри единичного круга на плоскости, заполняют всю плоскость, за исключением лишь луча на горизонтальной оси координат, начинающегося в точке с координатой — 1/4 и уходящего влево на бесконечность. При этом внутри круга нет двух точек, которые переводились бы функцией Кёбе в одну и ту же точку!

Если разложить функцию Кёбе в степенной ряд, выполнив формальное алгебраическое деление числителя на знаменатель, то получится ряд z + 2г2 + Зг3 + . У Бибербаха возникла смелая догадка: если функция задает взаимно-однозначное соответствие между точками единичного круга и точками некоторой односвязной плоской области, то коэффициенты степенного ряда, представляющего функцию,

 

63 Comments

  1. 658821 973794I really like your writing style truly enjoying this internet web site . 88924

  2. I couldn’t refrain from commenting. Perfectly written!

  3. Great work! That is the kind of info that should be shared across the web.
    Shame on Google for now not positioning this post higher! Come on over and talk over with
    my web site . Thank you =)

  4. It’s the best time to make a few plans for the long
    run and it’s time to be happy. I have read
    this publish and if I could I desire to recommend you some attention-grabbing things or tips.
    Maybe you could write subsequent articles relating to this article.
    I desire to read even more things approximately it!

  5. Pretty section of content. I just stumbled upon your web site
    and in accession capital to assert that I acquire in fact enjoyed account
    your blog posts. Any way I’ll be subscribing to your feeds and
    even I achievement you access consistently quickly.

  6. I am really impressed together with your writing talents as
    neatly as with the structure in your blog. Is this a paid subject matter or did you modify it your self?
    Anyway stay up the nice quality writing, it’s uncommon to
    peer a great weblog like this one today..

  7. Hello there! This article could not be written much better!

    Reading through this post reminds me of my previous roommate!
    He always kept talking about this. I’ll send this information to him.

    Pretty sure he’ll have a great read. Thank you
    for sharing!

  8. It’s wonderful that you are getting ideas from this article as well as from our discussion made here.

  9. Hey I am so glad I found your webpage, I really found you by mistake, while I was researching on Askjeeve for something else, Anyways
    I am here now and would just like to say many thanks
    for a incredible post and a all round interesting blog (I also love the theme/design),
    I don’t have time to read it all at the minute but I have saved it
    and also included your RSS feeds, so when I have time I will be
    back to read more, Please do keep up the awesome
    work.

  10. What’s up, I log on to your blogs daily. Your writing style is
    awesome, keep up the good work!

  11. Zora:

    Do you mind if I quote a couple of your posts as long as I provide credit and sources
    back to your webpage? My blog site is in the very same niche as yours
    and my users would really benefit from some of the information you provide here.
    Please let me know if this ok with you. Regards!

  12. Simply wish to say your article is as astounding. The clearness
    in your put up is just great and that i could assume you’re knowledgeable on this
    subject. Well with your permission let me to grasp your RSS feed to stay up to date with forthcoming
    post. Thank you one million and please carry on the gratifying work.

  13. I always spent my half an hour to read this web site’s articles or
    reviews every day along with a mug of coffee.

  14. great put up, very informative. I’m wondering
    why the other experts of this sector do not realize this.
    You must continue your writing. I’m sure, you’ve a great
    readers’ base already!

  15. Good day! Do you use Twitter? I’d like to follow you if that would be
    okay. I’m definitely enjoying your blog and look forward
    to new updates.

  16. I was able to find good information from your blog posts.

  17. Hi! I’m at work browsing your blog from my new apple iphone!
    Just wanted to say I love reading through your blog and
    look forward to all your posts! Keep up the superb work!

  18. I don’t even know how I ended up here, but I thought this post was great.
    I don’t know who you are but definitely you are going to a famous blogger if you aren’t
    already ;) Cheers!

  19. It’s a pity you don’t have a donate button! I’d definitely donate to this
    outstanding blog! I suppose for now i’ll settle for book-marking and adding your RSS feed to
    my Google account. I look forward to brand new updates and will talk about this website with my Facebook group.
    Chat soon!

  20. Excellent site. Lots of helpful info here. I’m sending it to several friends ans also sharing in delicious.
    And certainly, thank you on your sweat!

  21. Pretty! This has been an incredibly wonderful article.
    Thanks for providing these details.

  22. My partner and I absolutely love your blog and
    find many of your post’s to be exactly what I’m looking for.
    Do you offer guest writers to write content for yourself?
    I wouldn’t mind producing a post or elaborating on most
    of the subjects you write with regards to here. Again, awesome web site!

  23. Howdy exceptional blog! Does running a blog similar to this take a lot of work?
    I’ve virtually no understanding of computer programming but I
    was hoping to start my own blog soon. Anyhow, if you have any ideas or techniques for new blog owners
    please share. I know this is off subject nevertheless I simply needed to ask.
    Thank you!

  24. With havin so much content and articles do you ever run into any issues of plagorism or copyright infringement?
    My website has a lot of unique content I’ve either created myself or outsourced but it seems a lot of it is popping it up
    all over the internet without my authorization. Do you
    know any techniques to help stop content from being stolen? I’d definitely appreciate it.

  25. Asking questions are genuinely pleasant thing
    if you are not understanding something entirely, however this article gives
    good understanding even.

  26. Very good post. I’m facing a few of these issues
    as well..

  27. My programmer is trying to convince me to move to .net from PHP.
    I have always disliked the idea because of the costs.
    But he’s tryiong none the less. I’ve been using Movable-type on numerous websites for about a year and am nervous about switching to
    another platform. I have heard fantastic things about blogengine.net.
    Is there a way I can import all my wordpress content into it?
    Any kind of help would be really appreciated!

  28. Good article. I certainly love this site. Thanks!

  29. I every time used to study piece of writing in news
    papers but now as I am a user of web so from now I am using net for
    articles, thanks to web.

  30. Excellent way of telling, and pleasant article to get facts about
    my presentation subject, which i am going to convey in university.

  31. A motivating discussion is definitely worth comment. I think that you ought to publish more
    about this issue, it may not be a taboo subject but usually people don’t discuss
    such issues. To the next! All the best!!

  32. Nice post. I learn something totally new and challenging on websites I stumbleupon on a daily
    basis. It’s always helpful to read articles from other writers and
    use a little something from other web sites.

  33. Attractive section of content. I just stumbled upon your web
    site and in accession capital to say that I acquire actually loved account your blog posts.

    Anyway I will be subscribing on your augment and even I achievement you get right of
    entry to persistently quickly.

  34. My partner and I stumbled over here from a different web
    page and thought I may as well check things out.
    I like what I see so now i am following you. Look forward to finding out about your web page again.

  35. Heya! I understand this is sort of off-topic but I needed to ask.
    Does managing a well-established website such as yours take a massive amount work?
    I am completely new to operating a blog however I do write in my
    diary on a daily basis. I’d like to start a blog so I
    can easily share my personal experience and views online.
    Please let me know if you have any ideas or tips for new aspiring bloggers.
    Appreciate it!

  36. Very good blog you have here but I was wondering if you knew of any user discussion forums that cover
    the same topics discussed in this article? I’d really love to be
    a part of online community where I can get suggestions from other knowledgeable individuals
    that share the same interest. If you have any suggestions, please let me know.
    Thank you!

  37. Quality content is the main to be a focus for the viewers to pay a visit the web page, that’s
    what this site is providing.

  38. Thank you for the good writeup. It actually was once a
    amusement account it. Look advanced to more added agreeable
    from you! By the way, how could we communicate?

  39. A person essentially assist to make severely posts I’d state.
    That is the very first time I frequented your website page and to this
    point? I amazed with the analysis you made to make this
    particular post amazing. Excellent task!

  40. You’re so awesome! I do not suppose I have read a single thing like this before.
    So nice to find another person with unique thoughts on this issue.
    Seriously.. many thanks for starting this up. This site is one thing that is required on the internet, someone with some originality!

  41. I every time emailed this blog post page to all my contacts, since if like to read it afterward my friends will too.

  42. I was recommended this website by my cousin. I’m not
    sure whether this post is written by him as nobody else
    know such detailed about my difficulty. You’re wonderful!

    Thanks!

  43. This paragraph is actually a good one it helps new web users, who are wishing for
    blogging.

  44. Oh my goodness! Awesome article dude! Thank you so much, However I
    am going through troubles with your RSS. I don’t understand the reason why I am unable to join it.
    Is there anybody getting the same RSS problems? Anyone that
    knows the solution will you kindly respond? Thanks!!

  45. Good way of telling, and fastidious paragraph to
    get information regarding my presentation topic, which i am going to present in university.

  46. I just want to mention I am just all new to blogs and really loved your blog. Likely I’m going to bookmark your blog post . You really come with outstanding articles and reviews. Thank you for revealing your web site.

  47. Hello there, just became alert to your blog through Google, and
    found that it’s truly informative. I’m going to watch out
    for brussels. I will be grateful if you continue this in future.

    Lots of people will be benefited from your writing. Cheers!

  48. Hi there! I could have sworn I’ve visited this blog before but after looking at a few of the posts I realized
    it’s new to me. Anyways, I’m definitely pleased I stumbled upon it and I’ll
    be book-marking it and checking back often!

  49. Write more, thats all I have to say. Literally,
    it seems as though you relied on the video to make your point.

    You obviously know what youre talking about, why waste your intelligence on just posting videos to your site when you could be giving us something enlightening to read?

  50. Thank you, I have just been looking for information about this topic for a while and yours
    is the best I have discovered till now. However, what about the
    conclusion? Are you sure concerning the source?

  51. Hello, Neat post. There is an issue with your site in internet explorer, may test this?
    IE still is the marketplace leader and a huge component of other people will pass over your great writing because of this problem.

  52. I constantly emailed this blog post page to all my associates, because if like to read it after
    that my friends will too.

  53. Hello there, just became alert to your blog through Google, and found that it
    is truly informative. I’m gonna watch out for brussels. I will be grateful if you continue this in future.
    Lots of people will be benefited from your writing.

    Cheers!

  54. I visit each day some web sites and websites to read articles, except this
    webpage offers feature based posts.

  55. It’s really a great and helpful piece of info. I am glad that you shared this helpful information with us. Please keep us up to date like this. Thanks for sharing.

  56. Awesome! Its genuinely awesome article, I have got much clear idea about from
    this article.

  57. I think this is among the most vital information for me. And i’m glad reading your article. But wanna remark on some general things, The web site style is wonderful, the articles is really great : D. Good job, cheers

  58. Piece of writing writing is also a excitement, if you be familiar with then you
    can write or else it is complicated to write.

  59. I have been exploring for a little bit for any high quality articles or weblog posts in this kind of area . Exploring in Yahoo I eventually stumbled upon this web site. Studying this info So i am happy to express that I’ve an incredibly excellent uncanny feeling I found out exactly what I needed. I most no doubt will make certain to do not disregard this web site and give it a look regularly.

  60. Thanks a lot for providing individuals with an extremely special possiblity to read in detail from here. It can be so pleasing plus full of a great time for me and my office co-workers to search the blog no less than thrice in one week to find out the newest guides you have. And of course, I’m certainly fascinated with your amazing knowledge you give. Some 3 facts in this article are ultimately the most suitable I have ever had.

  61. Just desire to say your article is as amazing. The clarity in your post is just great and i could assume you’re an expert on this subject. Fine with your permission let me to grab your RSS feed to keep up to date with forthcoming post. Thanks a million and please keep up the gratifying work.

  62. You can certainly see your skills in the work you write.
    The arena hopes for more passionate writers like you who are not
    afraid to mention how they believe. At all times go after
    your heart.

  63. Hey there, I think your site might be having browser compatibility issues.
    When I look at your blog in Ie, it looks fine but when opening
    in Internet Explorer, it has some overlapping. I just wanted to give you a quick heads up!
    Other then that, great blog!

Оставить коментарий