The full title of circle method is „Hardy Lee Wood circle method”, not only studies the important instrument of Goldbach's conjecture, is the important instrument that in the analytic theory of numbers standing-by uses. 圆法的全称为“哈代・李特伍德圆法”,不但是研究哥德巴赫猜想的重要工具,更是解析数论中常备用到的重要工具。 But invention about this tool, not in Goldbach issue. The viewpoint that now the mathematics circles generally thinks is, this concept is Hardy in „asymptotic analysis of integer resolution” in issue first appears with Larmat Noojin research, then in Hardy and Li Te Wood cooperates to study Waring's problem, was supplemented completely. 而关于这个工具的发明,并非是在哥德巴赫问题上。现在数学界普遍认为的观点是,这一概念是哈代在与拉马努金研究“整数拆分的渐近分析”问题中最先出现的,而后在哈代与李特伍德合作研究华林问题时,被补充完整。 Now, as studying the important instrument of Goldbach's conjecture, this tool had been carried forward by the mathematicians of later generation. 如今,作为研究哥德巴赫猜想的重要工具,这项工具已经被后世的数学家发扬光大。 For example stands Herve Gott on platform, is in current theory of numbers, the big cow of circle method theory. 比如站在讲台上的赫尔夫戈特,便是当今数论界中,圆法理论的大牛。 „...... The connotation of Goldbach's conjecture to be bigger than 2 even numbers willfully may write the sums of two prime number, we call it to suspect for the time being.” “……哥德巴赫猜想的内涵为任意大于二的偶数都可写成两个质数之和,我们姑且称之为猜想a。” „......, because the odd number subtracts the wonderful prime number is an even number, suspected that A thinks any even number is equal to the sums of two prime number, therefore with suspecting A may result in the deduction to suspect B, was bigger than 9 odd numbers to write the sums of three wonderful prime number willfully.” “……由于奇数减去奇素数是一个偶数,猜想a认为任何偶数都等于两个素数之和,故而用猜想a可得推论猜想b,任意大于九的奇数都可以写成三个奇素数之和。” The beginning spoke in vain here, Herve Turton, continued. 开场白说到这里,赫尔夫戈特顿了顿,继续说。 „However I told ‚circle method’, was showed that the weak suspicion of its Goldbach's conjecture, namely suspected B!” “而我所讲述的‘圆法’,便是证明其哥德巴赫猜想的弱猜想,即猜想b！” Suspects a establishment, suspected that B establishes certainly. 猜想a成立,猜想b一定成立。 But in turn, is not good. 但反过来,却不行。 Why as, this involves to a logical mathematics in very interesting the issue. Is inenarrable with the elementary mathematics, words that but explained with the descriptive language, was „is bigger than the set that the 9 odd numbers and wonderful prime number sums of composed willfully”, this set was not equal to „any even number”, and all elements in happening together were infinite, may not exhaust the proof. 至于为什么,这涉及到一个逻辑数学中很有趣的问题。用初等数学难以描述,但用描述性的语言来解释的话,就是“任意大于九的奇数与奇素数之和”所组成的集合,与“任何偶数”这一集合不等价,且交集中的所有元素无限多,亦不可穷举证明。 Actually abstract, circle method „even number set” sieve method „1 + 1 forms”, everyone is the same, misses the final shooting. 其实抽象的来看,无论是圆法的“偶数集合”还是筛法的“1+1形式”,大家都是半斤八两,都差最后的临门一脚。 This distance is to possibly be away from a river, possibly is two mountains looks. 这个距离可能是隔着一条河,也可能是两山对望。 After brief prologue, Herve Gott rubbish, wrote down one line of mathematical formulas in the blank slate. 简短的开场白之后,赫尔夫戈特也不废话,在白板上写下了一行算式。 【......, when 2 n, there is ( n ) = 1 / 2 n ( n2 / n 3 ) n ( 1-1 / ( p-1 ) 2 ) n ( 1 + 1 / ( p-1 ) 2 ) , ( 1 + o ( 1 ) )】 【……当2n,有(n)=1/2n(n2/n3)n(1-1/(p-1)2)n(1+1/(p-1)2),(1+o(1))】 Sees this line of mathematical formulas brightly the instance, the Lu Zhou eye slightly one. 看到这行算式的瞬间,陆舟眼睛微微一亮。 This group of expression venerables scribble actually not conveniently, Hardy and Li Te Wood these double-digit discussed the big shot, in one of the numerous expressions 1922 in that paper proposing! 这行表达式倒不是老先生随手乱写的,正是哈代与李特伍德这两位数论界的大佬,在1922年那篇论文中提出的众多表达式之一！ When studies Twin Prime Conjecture, Lu Zhou has happen to consulted that literature, even has conducted the quotation to some conclusions. 在研究孪生素数猜想的时候,陆舟正好查阅过那篇文献,甚至对其中的部分结论进行过引用。 Also therefore, he could be said as the impression being profound to this. 也正是因此,他对这个可以说是印象深刻了。 It seems like this public lecture, Interesting. 看来这报告会,有点意思啊。 Stands the old man before blank slate does not say a word , to continue to take the symbol pen to write. 站在白板前的老头一言不发,继续在拿着记号笔唰唰唰地写着。 In conference site completely silent. 会场内鸦雀无声。 Not only a Lu Zhou hear of earnestness of , other arrive at the big shot also to listen is looking very much earnestly. 不只是陆舟听的很认真,就连其它到大佬们也听的很认真地在看。 The technique industry studies, even the big shot, impossible to penetrate in the flash into others' domain. Therefore generally paper in the public lecture, will emit in the conference official site ahead of time, prepares a lesson, will prepare to ask asked that paints in the note. 术业有专攻,即便是大佬,也不可能在一瞬间就深入到别人的领域中。所以一般报告会上的论文,都会在会议官网上提前放出,供人预习,将准备问的问题写在笔记上。 If the public lecture has not answered own question, is inquiring the link to propose the issue, this listens to the correct posture of academic conference, not only the past watched the fun and applauds purely has participated even. 如果报告会并没有解答自己的问题,在提问环节将问题提出,这才是听学术报告会的正确姿势,并不只是单纯地过去看个热闹、鼓个掌就算参加过了。 More than 40 minutes passes, Herve Gott stopped the symbol pen in hand, turns around to look to the conference site. 四十多分钟的时间过去,赫尔夫戈特停下了手中的记号笔,转身看向会场。 „Basic proof process was this, had the words of what issue, now can inquire.” “基本证明过程就是这样了,有什么问题的话,现在可以提问了。” Lu Zhou raised the hand. 陆舟举起了手。 Herve Gott and Lu Zhou to the line of sight, nodded, hint him to be able the speech. 赫尔夫戈特和陆舟对上了视线,点了点头,示意他可以起来发言。 Swept a note, Lu Zhou stood up, the inquiry said. 扫了眼笔记,陆舟站起身来,提问道。 „About the mathematical formula that your 34 th ranks have, I have the question. You to the operation of = ∑ a ( n ) z ^ n + δ ( n ), obtain each integer n > 0 directly. I guessed you use possibly is Kesey Gutha theorem or its deduction theorem of residues. But how are you estimate function f (s ) are the holomorphic function?” “关于您第34行列出的算式,我存在疑问。您对=∑a(n)z^n+δ(n)的运算中,直接得出每一个整数n>0。我猜测您用的可能是柯西-古萨定理或者它的推论留数定理。但你是如何判断函数f(s)是全纯函数？” In the conference site resounds the low voice discussion. 会场内响起小声议论。 Obviously, the question that Lu Zhou asked that asked in the hearts of many. 显然,陆舟问的这个问题,问到了不少人的心坎里。 „This issue asked very well,” Herve Gott looked at Lu Zhou one accidentally/surprisingly, turned around to write down one line of mathematical formulas in the blank slate, then the symbol pen knocked knocking above, „understood?” “这个问题问得很好,”赫尔夫戈特意外地看了陆舟一眼,转身在白板上写下了一行算式,然后记号笔在上面敲了敲,“懂了吗？” Sees that line of mathematical formulas, the Lu Zhou expression slightly suddenly, nods. 看到那行算式,陆舟表情略微恍然,点了点头。 „Understood, thanks.” “懂了,谢谢。” Nods politely, Lu Zhou sat, blank slate the mathematical formula of that line of supplements, copied conveniently in the notebook. 礼貌地点了点头,陆舟坐了回去,顺手将白板上的那行补充的算式,抄在了笔记本上。 Although he studies is mainly the sieve method, but the method of Herve Mr. Gott, has a big instructive to his research work. So-called research work also this, improves own theory in the exchange discussion, rubs the new viewpoint in the collision of thought. 虽然他研究的主要是筛法,但赫尔夫戈特先生的方法,对他的研究工作也有不小的启发性。所谓的研究工作也正是这样,在交流讨论中完善自己的理论,在思维的碰撞中摩擦出新的观点。 When the Lu Zhou reorganization note, some side people poked his arm gently. 就在陆舟整理笔记的时候,旁边有人轻轻戳了戳他胳膊。 „Sorry, can ask your question?” “对不起,可以问你一个问题吗？” What speech is a skin color is slightly pale, keeps a little miss of slightly volume blonde. 说话的是一位肤色略微苍白,留着一头微卷金发的小姑娘。 Reason that said is the little miss, because she seemingly young appearance, is shorter than Lu Zhou, was the undergraduate student of UC Berkeley...... must say that probably she was the words of graduate student, Lu Zhou did not believe in any case absolutely. 之所以说是小姑娘,因为她看上去年龄不大的样子,个头比陆舟矮一点,大概是加大伯克利分校的本科生……要说她是研究生的话,反正陆舟是绝对不信的。 Although her English pronunciation is somewhat jerky, but the sound is very light, accidental/surprised is a little of pleasant to hear. 虽然她的英语发音有些生涩,但声音很轻,意外的有点好听。 No matter the sound is of pleasant to hear, regarding Lu Zhou, some person and he discussed the mathematical problem, so long as did not create a scene, he will never reject, therefore then said very much naturally: „Asked.” 不管声音好不好听,对于陆舟而言,有人和他讨论数学问题,只要不是无理取闹,他是从来不会拒绝的,于是便很大方的说:“问吧。” The female student blinks, somewhat referred to the blank slate awkwardly, said: „Sorry, what that...... did you understand a moment ago?” 那女生眨了眨眼,有些尴尬指了指白板上,说:“对不起,那个……你刚才懂了什么？” Sees that line of mathematical formulas, she has not mastered completely. 看到那行算式,她完全没有搞懂。 „Are you is asking that expression?” Guessed correctly probably the question that she wants to ask, Lu Zhou explained very much patiently: „Because that line calculates that i ( n ) = ∫ \ { f (s ) /s ^ ( n + 1 ) } ds = 2 π ian in mathematical formula, this is close orbit General points, therefore returns original, can directly using the theorem of residues. The mentality that Professor Hull Gove explained possibly quite jumped, was not truly good to understand, must think.” “你是问那个表达式？”大概猜到了她想问的问题,陆舟很耐心地解释:“因为那行算算式中的i(n)=∫\{f(s)/s^(n+1)}ds=2πian,这是一个闭轨积分,所以回到原式中,可以直接运用留数定理。赫尔戈夫特教授讲解的思路可能比较跳跃,确实不好理解,得多想想。” Is listening to the explanation of Lu Zhou, this female student takes the note in the book flustered. 听着陆舟的讲解,这位女生慌慌张张地在本子上记着笔记。 From the technique of her recording note all affairs big or small, Lu Zhou believes firmly own guess, she is attending the undergraduate course probably. 从她那事无巨细的记笔记的手法,陆舟更确信了自己的猜测,她大概是在读本科。 However the undergraduate course listens to this course, really can understand? 不过本科听这种讲座,真的能听得懂吗？ Feared that she asked embarrassed, Lu Zhou spoke thoughtlessly: „What question also has?” 怕她不好意思问,陆舟随口:“还有什么疑问吗？” „Thanks, did not have...... to sorry, can give me your mailbox? Some of my also many issues want to ask...... you.” Because is extremely anxious, this seems like the somewhat rash female student, did not nip the tongue carefully red, the face. “谢谢,没有了……对不起,可以把您的邮箱给我吗？我还有很多问题想问……您。”因为太过紧张,这位看起来有些冒失的女生,不小心咬到了舌头,脸唰的红了起来。 Can look, she is not good at exchanging very much. 看得出来,她不是很擅长与人交流。 Similarly does not excel at the human relations specially, Lu Zhou can understand actually, therefore has not cared, spoke thoughtlessly saying: „Doesn't matter. Moreover, you were needless always to say ‚sorry’. My name was Lu Zhou, was your name?” 同样不是特别擅长交际,陆舟倒是能理解,所以也没有在意,随口说道:“没关系。另外,你不用总是说‘对不起’。我的名字叫陆舟,你的名字是？” „I know that you called Lu Zhou, I have seen you at the opening ceremony,” possibly suddenly thinks from the report name, that female student had not supplemented the sentence embarrassed, „my name was Vera, studied in Berkeley...... is interested in the pure mathematics very much, particularly theory of numbers direction.” “我知道您叫陆舟,我在开幕式上见过您,”可能是突然想起来自己还没自报姓名,那位女生不好意思地补充了句,“我叫薇拉,在伯克利读书……对纯粹数学很感兴趣,尤其是数论方向。” Vera? 薇拉？ Sounds is a bit like Hebrew, the Russian? 听起来有点像希伯来语,俄罗斯人？ Lu Zhou swept the eye subconsciously her chest front, although is insufficient the vast stretch of flat land, but truly was also poor. 陆舟下意识的扫了眼她的胸前,虽然不至于一马平川,但也确实寒酸了点。 emmm...... emmm…… Probably not? 大概不是吧？ „Takes the liberty to ask, are you big this year?” “冒昧问一下,你今年多大？” „17......” “17……” Some Lu Zhou surprise looked at her one eyes: „Can 17 years old on Berkeley?” 陆舟有些诧异地看了她一眼:“17岁能上伯克利吗？” This age, his high school has not graduated. 这个年龄,他高中还没毕业呢。 „I am the imo gold medal recommend for admission to school......” Vera to smile embarrassed, the tone somewhat admires said, „naturally, with has solved you of two conjectures to compare is not worth mentioning......” “我是imo金牌保送……”薇拉不好意思笑了笑,语气有些仰慕地说道,“当然了,和已经解决过两个数学猜想的您比起来不值一提……” Lu Zhou gawked, said: „......, The gold medal of Olympics math competition is not very strong, you can in self-confident, does not need to improperly belittle oneself. Surprising, did your 15 years old win the gold medal? You are in young high schools” 陆舟愣了下,说:“……不,奥林匹克数学竞赛的金牌已经很强了,你可以在自信一点,不用妄自菲薄。令人惊讶,你15岁就拿到了金牌？那你是几岁上的高中” At this moment, the last quizzer speaks, sees no one to continue to inquire, Herve Mr. Gott on stage then announced the public lecture ended. 就在这时,最后一位提问者发完言,见没有人继续提问,台上的赫尔夫戈特先生便宣布了报告会结束。 „About proves the Goldbach's conjecture completely, we have a long way to go.” “关于完全证明哥德巴赫猜想,我们还有很长的路要走。” „My public lecture arrived here, thanked appearance!” “我的报告会就到这里,感谢诸位到场！” Herve Gott signals by nodding slightly, walks toward the stage amid an applause. 赫尔夫戈特微微点头示意,在一片掌声中向台下走去。 Because oneself have not attended the imo competition, Lu Zhou is very interested. Originally he also plans and this little miss who wins the gold medal chatted several, but saw the time not early, his also a little matter must be done by chance, then placed this matter one side, tidied up begins a stroke to record, walked toward the conference site. 因为自己没有参加过imo大赛,陆舟还是挺感兴趣的。本来他还打算和这位拿到金牌的小姑娘聊几句,但见时间不早了,恰巧他还有点事情要做,便将这件事放在了一边,收拾起笔记,向会场外走去。