Riemann Hypothesis solved?

[jason1990]

http://arxiv.org/abs/math.NT/0703367

[djames]

Found any comments from other authors on this paper yet?

Couldn't the proof of lemma 1 have just gone like this? The number of zeros of the zeta function on the critical line in any finite interval is finite, hence the zeros are discrete, hence there are open intervals between them. Done!?

[jason1990]

I have not seen any comments on this yet. I think the point of Lemma 1 is that the constant A does not depend on n. So this is saying more than that the zeros are discrete. It is saying something about their asymptotic spacing.

[djames]

Well, sure. But his A depends on A1, and A1 is also independent of n. So, his full argument doesn't remove any dependences that the first sentence of his proof didn't. Thus, keeping his first sentence, and tacking on the above logic proves the lemma as stated.

Anyway, I'm just noting that 1) the choice of arxiv as the medium for which publication of a disproof of this magnitude was chosen, and 2) the seemingly unnecessary argument in the proof of the 1st lemma makes me lean towards this as lunatic ravings.

Of course it would be wonderful if this holds. May I reserve the right to not hold my breath?

[MelchyBeau]

djames,

the proof to the poincare conjecture was published on that site

[djames]

Ok, I take everything back. This paper is a gold-mine. Let's not even review it for accuracy. Riemann is false. Case closed. Well done. Nice hand. Next.

[Siegmund]

I'd be highly suspicious of the fact that the vast majority of his citations are either ancient articles or in the popular press. Hasn't there been ANY prior work on Riemann in the last 30 years or so? Also, a few things about the writing style suggest the writer hasn't submitted much to a math journal before, as opposed to just having english as a 2nd language.

I was made suspicious enough on a first skimming to not feel like investing effort in trying to remember enough analysis from 10 years ago to pick carefully through the proofs.

[jason1990]

For whatever this may be worth, MathSciNet shows 44 entries for "Items authored by Pati, Tribikram". They are

MR1972007 Dedication.
Analysis and applications (Ujjain, 1999),
v--vii, Narosa, New Delhi, 2002.


MR1970623 (2003k:00013) Analysis and applications.
Proceedings of a conference held in honor of Professor Tribikram Pati on
the occasion of his 70th birthday in Ujjain, 1999.
Edited by H. P. Dikshit and Pawan K. Jain.
Narosa Publishing House, New Delhi, 2002. xii+294 pp. ISBN: 81-7319-470-X


MR1970597 (2004e:40001) Pati, T. Extended Tauberian theorems.
Analysis and applications (Ujjain, 1999),
235--250, Narosa, New Delhi, 2002.


MR1880488 (2003a:40007) Pati, T. On the absolute Cesàro summability of Fourier series.
Indian J. Math. 43 (2001), no. 3, 323--339.


MR1836368 (2002c:40003) Pati, T. On a Tauberian theorem of Hardy and Littlewood.
Proc. Indian Acad. Sci. Math. Sci. 111 (2001), no. 2, 221--227.


MR1795831 (2001i:40004) Pati, T. Generalization of a theorem of Kogbetliantz on absolute
summability.
B. N. Prasad birth centenary commemoration volume, II.
Indian J. Math. 42 (2000), no. 1, 87--106.


MR1780890 Pati, T. On the convergence and summability $(C,1)$ of the Lebesgue-Fourier
series.
B. N. Prasad birth centenary commemoration volume.
Bull. Allahabad Math. Soc. 14 (1999), 95--103.


MR0234166 (38 #2485) Pati, T. A second theorem of consistency for absolute summability by discrete
Riesz means.
K\=odai Math. Sem. Rep. 20 1968 454--457.


MR0177258 (31 #1521) Pati, Tribikram . On the absolute summability of Fourier series by Nörlund means.
Math. Z. 88 1965 244--249.


MR0167779 (29 #5051) Pati, T. ; Ahmad, Z. U. A new proof of a theorem on the absolute summability factors of Fourier
series.
Riv. Mat. Univ. Parma (2) 4 1963 149--158.


MR0157180 (28 #417) Pati, Tribikram . On an unsolved problem in the theory of absolute summability factors of
Fourier series.
Math. Z. 82 1963 106--114.


MR0149193 (26 #6685) Pati, T. On the absolute Nörlund summability of the conjugate series of a
Fourier series.
J. London Math. Soc. 38 1963 204--214.


MR0161068 (28 #4277) Pati, T. ; Ramanujan, M. S. On iteration products preserving absolute convergence.
Boll. Un. Mat. Ital. (3) 17 1962 385--393.


MR0160061 (28 #3275) Pati, T. Effectiveness of absolute summability.
Math. Student 28 1962 177--187 (1962).


MR0155128 (27 #5068) Pati, T. Absolute Cesàro summability factors of infinite series.
Math. Z. 78 1962 293--297.


MR0154004 (27 #3964) Pati, T. ; Lal, S. N. The product of a logarithmic method and the sequence-to-sequence
quasi-Hausdorff method.
Proc. Japan Acad. 38 1962 432--437.


MR0147838 (26 #5351) Pati, T. A generalisation of a theorem of Wang on the summability of Fourier
series.
Indian J. Math. 4 1962 35--45.


MR0140885 (25 #4299) Pati, T. Addendum: "On the absolute Nörlund summability of a Fourier
series".
J. London Math. Soc. 37 1962 256.


MR0160060 (28 #3274) Pati, T. The second theorem of consistency for Riesz boundedness.
Math. Student 29 1961 101--112 (1962).


MR0160059 (28 #3273) Pati, T. A note on the second theorem of consistency for absolute
summability.
Math. Student 29 1961 93--100 (1962).


MR0152822 (27 #2796) Pati, T. The non-absolute summability of Fourier series by a Nörlund
method.
J. Indian Math. Soc. (N.S.) 25 1961 197--214.


MR0150530 (27 #527) Pati, T. A generalization of a theorem of Iyengar on the harmonic summability of
Fourier series.
Indian J. Math. 3 1961 85--90.


MR0138908 (25 #2348) Pati, T. On absolute summability by discrete Riesz means of type ${\rm
exp}\,(n)$ and order $2$.
J. Indian Math. Soc. (N.S.) 25 1961 27--32.


MR0136898 (25 #359) Prasad, B. N. ; Pati, T. On the multiplication of absolutely summable Dirichlet series.
J. Indian Math. Soc. (N.S.) 24 1960 421--431 (1961).


MR0124668 (23 #A1980) Pati, T. ; Ahmad, Z. U. On the absolute summability factors of infinite series. III.
Indian J. Math. 2 1960 73--87.


MR0123863 (23 #A1185) Pati, Tribikram ; Ahmad, Z. U. On the absolute summability factors of infinite series. I.
Tôhoku Math. J. (2) 12 1960 222--232.


MR0115039 (22 #5843) Prasad, B. N. ; Pati, T. The second theorem of consistency in the theory of absolute Riesz
summability.
Math. Ann. 140 1960 187--197.


MR0114070 (22 #4900) Pati, T. ; Ahmad, Z. U. On the absolute summability factors of infinite series. II.
Indian J. Math. 2 1960 29--39 (1960).


MR0113066 (22 #3907) Pati, T. Tauberian theorems for absolute Riesz summability.
Indian J. Math. 1 1959 61--68 (1959).


MR0111980 (22 #2838) Pati, T. On the absolute Cesàro summability of Fourier series of functions of
Lebesgue class $L\sp{p}$ and some related problems in the theory of Fourier
constants.
Ann. Mat. Pura Appl. (4) 47 1959 181--195.


MR0104098 (21 #2860) Pati, T. On the absolute Nörlund summability of a Fourier series.
J. London Math. Soc. 34 1959 153--160.


MR0111979 (22 #2837) Pati, T. ; Sinha, S. R. On the absolute summability factors of Fourier series.
Indian J. Math. 1 1958 no. 1 41--54 (1958).


MR0111978 (22 #2836) Pati, T. On the absolute Riesz summability of Fourier series, its conjugate
series and their derived series.
Proc. Nat. Inst. Sci. India. Part A 23 1957 354--369.


MR0095363 (20 #1866) Pati, T. Products of summability methods and Mercerian transformations.
Proc. Nat. Inst. Sci. India. Part A 23 1957 514--521.


MR0086159 (19,135a) Prasad, B. N. ; Pati, T. On the second theorem of consistency in the theory of absolute Riesz
summability.
Trans. Amer. Math. Soc. 85 (1957), 122--133.


MR0094648 (20 #1161) Pati, Tribikram . Contributions to the study of absolute summability of series.
Bull. Allahabad Univ. Math. Assoc. 17 1956/1957 18--30 (1958).


MR0065667 (16,465d) Pati, T. A Tauberian theorem for absolute summability.
Math. Z. 61, (1954). 75--78.


MR0064889 (16,351e) Pati, T. On the second theorem of consistency in the theory of absolute
summability.
Quart. J. Math., Oxford Ser. (2) 5, (1954). 161--168.


MR0063457 (16,124d) Pati, T. Products of summability methods.
Proc. Nat. Inst. Sci. India 20, (1954). 348--351.


MR0062260 (15,952d) Pati, T. On the absolute Riesz summability of Fourier series and its conjugate
series.
Trans. Amer. Math. Soc. 76, (1954). 351--374.


MR0062247 (15,950e) Pati, T. The summability factors of infinite series.
Duke Math. J. 21, (1954). 271--283.


MR0058004 (15,306f) Pati, T. On the absolute Riesz summability of Fourier series and its conjugate
series.
Bull. Calcutta Math. Soc. 44, (1952). 155--168.


MR0051958 (14,553a) Pati, T. On the absolute summability of the conjugate series of a Fourier
series.
Proc. Amer. Math. Soc. 3, (1952). 852--857.


MR0044440 (13,420j) Pati, Tribikram . The development of non-Euclidean geometry during the last 150
years.
Bull. Allahabad Univ. Math. Assoc. 15, (1951). 1--8.

[djames]

Again, I hope it pans out. Given the number of publications, I guess I would have expected a little more as far as editing & independent author sponsorship. Perhaps these are valued more by some than others. From the first entry in your list, it appears he's pushing 80. I would also assume with that amount of mathematical experience these types of things would be second nature. Especially on a work of such importance.

[ErnestoHuaman]

Quoted from Djames:
"Anyway, I'm just noting that 1) the choice of arxiv as the medium for which publication of a disproof of this magnitude was chosen, and 2) the seemingly unnecessary argument in the proof of the 1st lemma makes me lean towards this as lunatic ravings.
Of course it would be wonderful if this holds. May I reserve the right to not hold my breath?"

Now, can you let us reserve the right not to have our reasoning disturbed by your big stinking mouth?
Think before speak.