# Books about the Riemann Hypothesis

I hope this question is appropriate for this forum. I am compiling a list of all books about the Riemann Hypothesis and Riemann's Zeta Function. Here is my list:

The Riemann Hypothesis: A Resource for the Afficionado and Virtuoso Alike, Peter Borwein, Stephen Choi, Brendan Rooney, Andrea Weirathmueller (Eds.)

The Riemann Hypothesis and Hilbert's Tenth Problem, by S. Chowla

Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics, by John Derbyshire

The Music of the Primes: Searching to Solve the Greatest Mystery in Mathematics, by Marcus du Sautoy

Riemann's Zeta Function, by Harold M. Edwards

The Riemann Zeta-Function: Theory and Applications, by Aleksandar Ivic

The Riemann Zeta-Function, by Anatoly A. Karatsuba and S. M. Voronin

In Search of the Riemann Zeros, by Michel L. Lapidus

Limit Theorems for the Riemann Zeta-Function, by Antanas Laurincikas

The Lerch zeta-function, by Antanas Laurincikas and Ramunas Garunkstis

Spectral Theory of the Riemann Zeta-Function, by Yoichi Motohashi

An Introduction to the Theory of the Riemann Zeta-Function, by S. J. Patterson

Stalking the Riemann Hypothesis: The Quest to Find the Hidden Law of Prime Numbers, by Dan Rockmore

The Riemann Hypothesis: The Greatest Unsolved Problem in Mathematics, by Karl Sabbagh

Seminar on the Riemann Zeta Function 1965-1966, by Robert Spira

Zeta and q-Zeta Functions and Associated Series and Integrals, by H. M. Srivastava and Junesang Choi

The Theory of the Riemann Zeta-Function, by E. C. Titchmarsh, D. R. Heath-Brown (Ed.)

Zeta Functions over Zeros of Zeta Functions, by André Voros

Are any books missing from my list? I don't include books by mathematical cranks (especially books by amateurs who claim to prove RH in their book). I also don't include books about analytic number theory in general that include some material about the Riemann Hypothesis or Riemann's Zeta Function. I did not include books about related topics, such as zeta functions of groups. I realize that one could quibble about the inclusion of some of the books on my list, such as Laurincikas's book about the Lerch Zeta Function. I would be very grateful for any additions to my list.

Edit: Excluding books that consist of collections of mathematical tables, and books that are paper-length (say, under 50 pages), the following books can be added to my list:

Ramanujan Lecture Notes Series, Vol. 2: The Riemann zeta function and related themes (Proceedings of the international conference held at the National Institute of Advanced Studies, Bangalore, December 2003), R. Balasubramanian, K. Srinivas (Eds.), 206 pp.

Lectures on the Riemann zeta-function (1962), by K. Chandrasekharan, 148 pp.

Gavrilov, N. I. Problema Rimana o raspredelenii korneidzetafunktsii. (Russian) [The Riemann problem on the distribution of the roots of the zeta function ] Izdat. L'vov. Univ., Lvov, 1970 1970 172 pp.

Ivic, A. Lectures on mean values of the Riemann zeta function. Tata Institute of Fundamental Research Lectures on Mathematics and Physics, 82. Published for the Tata Institute of Fundamental Research, Bombay; by Springer-Verlag, Berlin, 1991. viii+363 pp. ISBN: 3-540-54748-7

Fractal Geometry and Number Theory: Complex Dimensions of Fractal Strings and Zeros of Zeta Functions, by Michel L. Lapidus and Machiel van Frankenhuysen, 1999

Fractal Geometry, Complex Dimensions and Zeta Functions: Geometry and Spectra of Fractal Strings, by Michel L. Lapidus and Machiel van Frankenhuysen, 2006

Ramachandra, K. On the mean-value and omega-theorems for the Riemann zeta-function. Tata Institute of Fundamental Research Lectures on Mathematics and Physics, 85. Published for the Tata Institute of Fundamental Research, Bombay; by Springer-Verlag, Berlin, 1995. xiv+169 pp. ISBN: 3-540-58437-4

History of Zeta Functions, by Robert Spira, 3 volumes, 1218 pages, 1999

Van der Veen, Roland; van de Craats, Jan De Riemann-hypothese. (Dutch) [The Riemann hypothesis] Een miljoenenprobleem. [A million dollar problem] Epsilon Uitgaven, Utrecht, 2011. vi+102 pp. ISBN: 978-90-5041-126-4

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I wonder if it would fit protocols better to post this as an answer after posting a short question that it answers. – Michael Hardy Feb 6 at 17:33
That will be a long list... consider writing it up as a BIBTeX bibliography. – vonbrand Feb 6 at 17:34
+1 on each of these The Riemann Hypothesis: A Resource for the Afficionado and Virtuoso Alike, by Peter Borwein, Stephen Choi, Brendan Rooney, Andrea Weirathmueller (Eds.) Riemann's Zeta Function, by Harold M. Edwards – Peter Sheldrick Feb 6 at 17:35
the Marcus du Sautoy stuff is more general audience – Peter Sheldrick Feb 6 at 17:36
@vonbrand There are probably a few books missing, but I doubt more than 5-10 at most. I have been collecting books about this topic for years and own copies of all the books on my list except for the two by Laurincikas as I cannot find reasonably priced copies of them. One book I could have included but chose not to is Infirmation de l'hypothèse de Riemann by Henri Berliocchi, who is a respected French economist but apparently claims to disprove RH in the book. – Marko Amnell Feb 6 at 18:46

Some of these are paper-length, not book-length, but they come up when I search Math Reviews for books, and who am I to argue with Math Reviews?

MR2934277 Reviewed van der Veen, Roland; van de Craats, Jan De Riemann-hypothese. (Dutch) [The Riemann hypothesis] Een miljoenenprobleem. [A million dollar problem] Epsilon Uitgaven, Utrecht, 2011. vi+102 pp. ISBN: 978-90-5041-126-4

MR2198605 Reviewed Jandu, Daljit S. The Riemann hypothesis and prime number theorem. Comprehensive reference, guide and solution manual. Infinite Bandwidth Publishing, North Hollywood, CA, 2006. 188 pp. ISBN: 0-9771399-0-5 11M26 (11N05) [From the publisher's description: "The author adopts the real analysis and technical basis to guide and solve the problem based on high school mathematics.''] [This one may not pass the "crank" test...]

MR1332493 Reviewed Ramachandra, K. On the mean-value and omega-theorems for the Riemann zeta-function. Tata Institute of Fundamental Research Lectures on Mathematics and Physics, 85. Published for the Tata Institute of Fundamental Research, Bombay; by Springer-Verlag, Berlin, 1995. xiv+169 pp. ISBN: 3-540-58437-4

MR1230387 Reviewed Ivić, A. Lectures on mean values of the Riemann zeta function. Tata Institute of Fundamental Research Lectures on Mathematics and Physics, 82. Published for the Tata Institute of Fundamental Research, Bombay; by Springer-Verlag, Berlin, 1991. viii+363 pp. ISBN: 3-540-54748-7

MR0747304 Reviewed van de Lune, J. Some observations concerning the zero-curves of the real and imaginary parts of Riemann's zeta function. Afdeling Zuivere Wiskunde [Department of Pure Mathematics], 201. Mathematisch Centrum, Amsterdam, 1983. i+25 pp.

MR0683287 Reviewed Klemmt, Heinz-Jürgen Asymptotische Entwicklungen für kanonische Weierstraßprodukte und Riemanns Überlegungen zur Nullstellenanzahl der Zetafunktion. (German) [Asymptotic expansions for canonical Weierstrass products and Riemann's reflections on the number of zeros of the zeta function] Nachrichten der Akademie der Wissenschaften in Göttingen II: Mathematisch-Physikalische Klasse 1982 [Reports of the Göttingen Academy of Sciences II: Mathematics-Physics Section 1982], 4. Akademie der Wissenschaften in Göttingen, Göttingen, 1982. 24 pp.

MR0637204 Reviewed van de Lune, J.; te Riele, H. J. J.; Winter, D. T. Rigorous high speed separation of zeros of Riemann's zeta function. Afdeling Numerieke Wiskunde [Department of Numerical Mathematics], 113. Mathematisch Centrum, Amsterdam, 1981. ii+35 pp. (loose errata).

MR0541033 Reviewed te Riele, H. J. J. Tables of the first 15000 zeros of the Riemann zeta function to 28 significant digits, and related quantities. Afdeling Numerieke Wiskunde [Department of Numerical Mathematics], 67. Mathematisch Centrum, Amsterdam, 1979. 155 pp. (not consecutively paged).

MR0565985 Reviewed van de Lune, J. On a formula of van der pol and a problem concerning the ordinates of the non-trivial zeros of Riemann's zeta function. Mathematisch Centrum, Afdeling Zuivere Wiskunde, ZW 16/73. Mathematisch Centrum, Amsterdam, 1973. iii+21 pp.

MR0359258 Reviewed \cyr Voĭtovich, N. N.; \cyr Nefedov, E. I.; \cyr Fialkovskiĭ, A. T. \cyr Pyatiznachnye tablitsy obobshchennoĭ dzeta-funktsii Rimana ot kompleksnogo argumenta. (Russian) [Five-place tables of the generalized Riemann zeta-function of a complex argument] With an English preface. Izdat. Nauka'', Moscow, 1970. 191 pp.

MR0266875 Reviewed Gavrilov, N. I. \cyr Problema Rimana o raspredelenii korneĭdzetafunktsii. (Russian) [The Riemann problem on the distribution of the roots of the zeta function ] Izdat. Lʹvov. Univ., Lvov, 1970 1970 172 pp.

MR0117905 Reviewed Haselgrove, C. B.; Miller, J. C. P. Tables of the Riemann zeta function. Royal Society Mathematical Tables, Vol. 6 Cambridge University Press, New York 1960 xxiii+80 pp.

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 Thanks. The two books that stand out are the ones by Ramachandra and Ivic. The rest seem to be paper-length, collections of tables or in languages I cannot read. Ivic's book seems to be out of print. While looking for copies on Amazon, I stumbled on another book: Ramanujan Lecture Notes Series, Vol. 2: The Riemann zeta function and related themes: Proceedings of the international conference held at the National Institute of Advanced Studies, Bangalore, December 2003. If one includes conference proceedings, there are probably more like that one. – Marko Amnell Feb 7 at 5:37 I found a few more by searching the Library of Congress Online Catalog: Alden McClellan, Summing the Riemann zeta function (1966); Alden McClellan, Riemann zeta function to high precision (1968); K. Ramachandra, Riemann zeta-function: Introductory lectures (1979); K. Chandrasekharan, Lectures on the Riemann zeta-function (1962). – Marko Amnell Feb 7 at 6:33 One more from the Library of Congress: Paul Turán, On some approximative Dirichlet-polynomials in the theory of the zeta-function of Riemann (1948), but it is only 36 pages. The two by Alden McClellan are both under 20 pages. How long does a book have to be to qualify as a book? It's a question I didn't consider... – Marko Amnell Feb 7 at 6:48