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リーマン予想の証明

Riemann予想の証明を宣言している論文(プレプリント、Webページ)を集めます。取り下げられたもの、間違っていると指摘されているものについても掲載しています。情報提供があると嬉しいです*1

最終更新日 2017/8/30

2017年

Frank Stenger
arXiv [v1] Thu, 3 Aug 2017, [v2] Mon, 14 Aug 2017
[1708.01209] Proof of the Riemann hypothesis

Vladimir Blinovsky
arXiv [v1] Mon, 13 Mar 2017, [v5] Mon, 1 May 2017
[1703.03827] Proof of Riemann hypothesis

2016年

Murad Ahmad Abu Amr
arXiv Sat, 12 Nov 2016
[1612.02664] A Proof of the Riemann Hypothesis and Determination of the Relationship Between Non- Trivial Zeros of Zeta Functions and Prime Numbers

Yuyang Zhu
arXiv Sat, 24 Sep
[1609.07555] Study of an Equivalent Proposition of Riemann Hypothesis

K. Eswaran
arXiv [v1] Sun, 11 Sep 2016, [v9] Tue, 4 Jul 2017
[1609.06971] The Dirichlet Series for the Liouville Function and the Riemann Hypothesis

Shaoyong Lai
arXiv [v1] Mon, 8 Aug 2016, [v8] Mon, 21 Aug 2017
[1608.03199v1] The rightness of the Riemann hypothesis
[v8]のコメント: The paper is totally wrong

M. R. Pistorius
arXiv [v1] Thu, 4 Aug 2016, [v3] Thu, 2 Feb 2017
[1608.01555v3] On the zeros of the zeta function and eigenvalue problems
This paper has been withdrawn by the author.

Alfred Wünsche
arXiv Sat, 9 Jul
[1607.04551] Approach to a Proof of the Riemann Hypothesis by the Second Mean-Value Theorem of Calculus

Kimichika Fukushima
arXiv [v1] Mon, 11 Jan 2016, [v7] Mon, 27 Feb 2017
[1602.03553] Proof that the real part of all non-trivial zeros of Riemann zeta function is 1/2

2015年

Reda Mohamed Ahmed Mahmoud
"New definition of the imaginary unit and proof of the riemann hypothesis"
in Global Journal of Pure and Applied Mathematics 11(1): 367-375.
証明のKey pointは-\frac{1}{12}=-\frac{1}{2}を示す部分です。

Michele Fanelli, Alberto Fanelli
arXiv [v1] Tue, 1 Sep 2015, [v4] Sun, 25 Jun 2017
[1509.01554] With Columbus: "buscar el levante por el ponente" and with Alice's backward walk: Verifying the Riemann hypothesis by falsifying its counter-hypothesis

Nianrong Feng, Yongzheng Wang, Ruixin Wu
arXiv [v1] Fri, 7 Aug 2015, [v5] Sat, 21 Jan 2017
[1508.02932] All of zeros of Riemann's Zeta-function are on $\sigma=1/2$

Jeonwon Kim
arXiv [v1] Thu, 30 Jul 2015, [v2] Tue, 24 May 2016
[1508.00533] A proof of the Riemann hypothesis using the remainder term of the Dirichlet eta function

2014年

JinHua Fei*2
arXiv Thu, 17 Jul 2014
[1407.4545] Riemann hypothesis is not correct

S.V. Matnyak*3
arXiv [v1] Tue, 22 Apr 2014, [v2] Thu, 23 Jul 2015
[1404.5872] Proof of the Riemann's hypothesis

Daniel E. Borrajo Gutiérrez
arXiv [v1] Tue, 15 Apr 2014, [v2] Mon, 28 Apr 2014
[1404.4333] On the Riemann Hypothesis and its generalizations

Jin Gyu Lee*4
Sun, 9 Feb 2014
[1402.2822] The Riemann Hypothesis and the possible proof

2013年

Agostino Prástaro*5
arXiv [v1] Tue, 28 May 2013, [v10] Tue, 27 Oct 2015
[1305.6845] The Riemann hypothesis proved

Bertrand Barrau
arXiv [v1] Wed, 22 May, [v4] Sat, 21 Sep 2013
[1305.5726v1] Hilbert-Polya conjecture and Generalized Riemann Hypothesis
Article withdraw as function Bs presented is not square integrable as claimed. (Mistake is on one sub-domain considered: function I2 near y=0)

Jin Gyu Lee
arXiv Thu, 2 May 2013
[1305.0323] Zeros of the Riemann Zeta Function

2012年

Gerasimos Pergaris
arXiv [v1] Tue, 4 Dec 2012, [v2] Sat, 21 Sep 2013
[1212.1413v1] On the Riemann Hypothesis
This paper has been withdrawn by the author due to a crucial error on last page: The choice of the functions F and G does not meet condition 4 of Theorem 2

Zeraoulia Elhadj
arXiv [v1] Sun, 30 Sep 2012, [v13] Wed, 1 Jul 2015
[1210.1517] A positive answer to the Riemann hypothesis: A new result predicting the location of zeros
This paper has been withdrawn by the author due to a crucial sign error in equation 1

Dmitry Pozdnyakov
arXiv [v1] Thu, 9 Feb 2012, [v5] Thu, 27 Aug 2015
[1202.2115] Physical interpretation of the Riemann hypothesis
"But it is undecidable and must be considered as an axiom."

J. G. Andrews
arXiv [v1] Tue, 3 Jan 2012, [v2] Mon, 24 Mar 2014
[1201.1810] Potential flow in the critical strip and the Riemann hypothesis

2010年

Michel Planat
arXiv [v1] Thu, 14 Oct 2010, [v2] Sat, 23 Oct 2010
[1010.3239] Riemann hypothesis from the Dedekind psi function

Ilgar Sh. Jabbarov
arXiv [v1] Mon, 31 May 2010, [v4] Wed, 14 Aug 2013
[1006.0381] The Riemann Hypothesis

2009年

Dorin Ghisa
arXiv [v1] Mon, 11 May 2009, [v4] Tue, 14 Feb 2012
[0905.1527] Riemann Zeta Function

Ruiming Zhang
arXiv [v1] Thu, 25 Jun 2009, [v20] Sun, 26 Jun 2016
[0906.4604] Proof of Riemann Hypothesis and Generalized Riemann Hypothesis

Raghunath Acharya
arXiv Mon, 23 Mar 2009
[0903.3973] Concerning Riemann Hypothesis

Julio Alcantara-Bode
arXiv [v1] Tue, 3 Feb 2009, [v2] Fri, 6 Feb 2009
[0902.0617] A proof of the Riemann Hypothesis
This paper has been withdrawn by the author, due to a crucial error in page 5.

2008年

Arne Bergstrom*6
arXiv [v1] Tue, 30 Sep 2008, [v18] Mon, 14 Oct 2013
[0809.5120] Proof of Riemann's zeta-hypothesis

Xian-Jin Li
arXiv [v1] Tue, 1 Jul 2008, [v4] Sun, 6 Jul 2008
[0807.0090] A proof of the Riemann hypothesis
This paper has been withdrawn by the author, due to a mistake on page 29.

Fu-Gao Song
arXiv [v1] Fri, 4 Jan 2008, [v2] Tue, 12 Jan 2010
[0801.0633] From Bombieri's Mean Value Theorem to the Riemann Hypothesis

2007年

Lev Aizenberg*7
arXiv [v1] Sun, 30 Dec 2007, [v2] Sat, 5 Jan 2008
[0801.0114] Lindel\"of's hypothesis is true and Riemann's one is not
The paper is withdrawn by the author.

Andrzej Madrecki
arXiv Mon, 10 Sep 2007
[0709.1389] One page proof of the Riemann hypothesis

Andrzej Madrecki
arXiv Fri, 27 Jul
[0707.4196] A short Brownian motion proof of the Riemann hypothesis

Andrzej Madrecki
arXiv Wed, 13 Jun 2007
[0706.1968] The Riemann hypothesis - an elementary analytic approach based on complex Laplace transform

Jinzhu Han
arXiv [v1] Wed, 13 Jun 2007, [v9] Thu, 3 Nov 2016
[0706.1929] Proof of Riemann Hypothesis

Jinzhu Han*8
arXiv [v1] Mon, 8 Jan 2007, [v2] Sun, 26 Oct 2008
[math/0701235] Proof of the Hilbert's Eighth Problem

2006年

Sze Kui Ng*9
arXiv [v1] Sun, 12 Mar 2006, [v2] Fri, 28 Sep 2012
[math/0603275] Quantum Knots and Riemann Hypothesis

2004年

Jailton C. Ferreira
arXiv [v1] Thu, 27 May 2004, [v20] Sun, 26 Apr 2015
[math/0405531] The non-trivial zeros of Riemann's zeta-function

2003年

Craig Alan Feinstein*10
arXiv [v1] Tue, 23 Sep 2003, [v4] Wed, 23 Nov 2011
[math/0309367] The Riemann Hypothesis is Unprovable

Kaida Shi
arXiv Thu, 10 Jul 2003
[math/0307136] A Geometric Proof of Riemann Hypothesis

2002年

Carlos Castro, Jorge Mahecha
arXiv [v1] Fri, 30 Aug 2002, [v3] Tue, 5 Nov 2002
[hep-th/0208221] Final steps towards a proof of the Riemann hypothesis

2001年

Matti Pitkanen
arXiv [v1] Tue, 11 Sep 2001, [v2] Mon, 26 Nov 2001
[math/0109072v1] A further step in the proof of Riemann hypothesis
Paper has been withdrawn due to an error in the basic argument that the states corresponding to the zeros of Riemann Zeta with Re[s]<1/2 allow a Fourier expansion in the basis provided by the states having Re[s]>= 1/2.

Matti Pitkanen
arXiv [v1] Mon, 5 Feb 2001, [v10] Mon, 5 Mar 2001
[math/0102031] Riemann hypothesis and super-conformal invariance
"replacement of the original claim that Riemann hypothesis has been proven with the statement that superconformal invariance implies Riemann hypothesis"

1999年

Chengyan Liu
arXiv Sat, 25 Sep 1999
[math/9909153] Riemann Hypothesis

*1:Twitterでお願いします。ここに載っていないものや、載っているが証明は宣言されていないのでは?というものについてはご指摘いただけると幸いです。

*2:否定的解決

*3:[v2]ではタイトルが"The Generalized Riemann's hypothesis"に変更されていて、一般化Riemann予想も証明したと主張しています。また、BSD予想解決論文もあります: arXiv Fri, 6 Jun 2014 [1406.2270] The proof of the correctness of the Birch and Swinnerton-Diyer conjecture

*4:Jacques Gélinasによる反証論文 arXiv [v1] Mon, 20 May 2013, [v2] Wed, 30 Jul 2014 [1305.4614] Note on a proposed proof of the Riemann Hypothesis by Jin Gyu Lee

*5:タイトルが私の英語力だと「リーマン予想は証明した」になってしまいます。

*6:論文21ページ+FAQ64ページ

*7:Riemann予想が成り立たないことの証明。

*8:Riemann予想だけでなく、一般化Riemann予想、Goldbach予想、双子素数予想を同時に解決しています。

*9:Goldbach予想と双子素数予想を解決した論文:arXiv Tue, 28 Mar 2006 [math/0603664] On a Proof of the Goldbach Conjecture and the Twin Prime Conjecture Poincaré予想を解決した論文:arXiv [v1] Tue, 15 Aug 2000, [v6] Mon, 31 Jul 2006 [math/0008103] Quantum invariants of 3-manifolds and Poincar\'{e} conjecture

*10:Riemann予想の証明不可能性