Relevant bibliographies by topics / Riemann hypothesis

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Riemann hypothesis'

Author: Grafiati
Published: 4 June 2021
Last updated: 25 July 2025

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Journal articles on the topic "Riemann hypothesis"

1

Durmagambetov, Asset A. "Riemann Hypothesis." Journal of Applied Mathematics and Physics 05, no. 07 (2017): 1424–30. http://dx.doi.org/10.4236/jamp.2017.57117.

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Suman, Shekhar, and Raman Kumar Das. "A NOTE ON AN EQUIVALENT OF THE RIEMANN HYPOTHESIS." JOURNAL OF RAMANUJAN SOCIETY OF MATHEMATICS AND MATHEMATICAL SCIENCES 10, no. 01 (2022): 97–102. http://dx.doi.org/10.56827/jrsmms.2022.1001.8.

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In this manuscript we denote by P ρ a sum over the non trivial zeros of Riemann zeta function (or over the zeros of Riemann’s xi function), where the zeros of multiplicity k are counted k times. We prove a result that the Riemann Hypothesis is true if and only if
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Ravindran, Renuka. "The Riemann hypothesis." Resonance 11, no. 11 (2006): 40–47. http://dx.doi.org/10.1007/bf02834472.

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Whitley, Robert. "The Riemann Hypothesis, the Generalized Riemann Hypothesis, and the Cesáro Operator." Integral Equations and Operator Theory 61, no. 3 (2008): 433–48. http://dx.doi.org/10.1007/s00020-008-1594-5.

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Haight, David F. "Summa characteristicaand the Riemann hypothesis: scaling Riemann’s mountain." Journal of Interdisciplinary Mathematics 11, no. 6 (2008): 851–901. http://dx.doi.org/10.1080/09720502.2008.10700605.

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Galetto, Fausto. "Riemann’s Hypothesis New Proof." Applied Science and Innovative Research 6, no. 1 (2022): p14. http://dx.doi.org/10.22158/asir.v6n1p14.

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After some papers proving the RC (short for “Riemann’s Conjecture”, also known as the “Riemann’s Hypothesis”, RH), now the author provides a new proof, using the “Spira Criterion” that states “The RH is equivalent to the statement that if s>0.5 and t> 6.5 then |z(1-s)|> |z(s)|”. We use the concept of “transfer function” for control systems. This new proof is so simple that the author wonders why a great mathematician like Riemann did not see it; therefore F. Galetto thinks that somewhere in the purported proof there should be an error.
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Bayer, Pilar. "La hipòtesi de Riemann: El gran repte pendent." Mètode Revista de difusió de la investigació, no. 8 (June 5, 2018): 35. http://dx.doi.org/10.7203/metode.0.8903.

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The Riemann hypothesis is an unproven statement referring to the zeros of the Riemann zeta function. Bernhard Riemann calculated the first six non-trivial zeros of the function and observed that they were all on the same straight line. In a report published in 1859, Riemann stated that this might very well be a general fact. The Riemann hypothesis claims that all non-trivial zeros of the zeta function are on the the line x = 1/2. The more than ten billion zeroes calculated to date, all of them lying on the critical line, coincide with Riemann’s suspicion, but no one has yet been able to prove
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Deloin, R. "Proof of Riemann Hypothesis." Asian Research Journal of Mathematics 9, no. 1 (2018): 1–8. http://dx.doi.org/10.9734/arjom/2018/40341.

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Fei, Jinhua. "About the Riemann Hypothesis." Journal of Applied Mathematics and Physics 04, no. 03 (2016): 561–70. http://dx.doi.org/10.4236/jamp.2016.43061.

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Mazurkin, P. M. "Proof the Riemann Hypothesis." American Journal of Applied Mathematics and Statistics 2, no. 2 (2014): 53–59. http://dx.doi.org/10.12691/ajams-2-2-1.

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Dissertations / Theses on the topic "Riemann hypothesis"

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Aronsson, Carl, and Gösta Kamp. "The Riemann Hypothesis." Thesis, KTH, Matematik (Inst.), 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-127725.

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The Riemann hypothesis was first proposed by Bernhard Riemann in 1860 [1] and says all non-trivial zeroes to the Riemann zeta function lie on the line with the real part 12 in the complex plane [1]. If proven to be true this would give a much better approximation of the number of prime numbers less than some number X. The Riemann hypothesis is regarded to be one of the most important unsolved mathematical problems. It is one of the Clay InstituteMilleniumproblems and originally one of the unsolved problems presented by David Hilbert as essential for 20th century mathematics at International C
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Henderson, Cory. "Exploring the Riemann Hypothesis." Kent State University / OhioLINK, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=kent1371747196.

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Juchmes, Franziska. "Zeta Functions and Riemann Hypothesis." Thesis, Linnéuniversitetet, Institutionen för matematik (MA), 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-32363.

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In this thesis the zeta functions in analytic number theory are stud-ied. The distribution of primes and the connection between primes andzeta functions are discussed. Numerical results for linear combinationsof zeta functions are presented. These functions have a symmetric dis-tribution of zeros around the critical line.
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Bielik, Alexander. "An introduction to the Riemann hypothesis." Thesis, KTH, Matematik (Inst.), 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-153636.

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This paper exhibits the intertwinement between the prime numbers and the zeros of the Riemann zeta function, drawing upon existing literature by Davenport, Ahlfors, et al. We begin with the meromorphic continuation of the Riemann zeta function ζ and the gamma function Γ . We then derive a functional equation that relates these functions and formulate the Riemann hypothesis. We move on to the topic of nite-ordered functions and their Hadamard products. We show that the xi function ξ is of finite order, whence we obtain many useful properties. We then use these properties to and a zero-free regi
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Nawaz, Daud. "The Dirichlet Series To The Riemann Hypothesis." Thesis, Högskolan i Gävle, Avdelningen för elektronik, matematik och naturvetenskap, 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:hig:diva-27028.

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This paper examines the Riemann zeta-function and its relation to the prime distribution. In this work, I present the journey from the Dirichlet series to the Riemann hypothesis. Furthermore, I discuss the prime counting function, the Riemann prime counting function and the Riemann explicit function for distribution of primes. This paper explains that the non-trivial zeros of the zeta-function are the key to understand the prime distribution.
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Tarkhanov, Nikolai. "A simple numerical approach to the Riemann hypothesis." Universität Potsdam, 2012. http://opus.kobv.de/ubp/volltexte/2012/5764/.

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The Riemann hypothesis is equivalent to the fact the the reciprocal function 1/zeta (s) extends from the interval (1/2,1) to an analytic function in the quarter-strip 1/2 < Re s < 1 and Im s > 0. Function theory allows one to rewrite the condition of analytic continuability in an elegant form amenable to numerical experiments.
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Bradford, Alexander. "Automated Conjecturing Approach to the Discrete Riemann Hypothesis." VCU Scholars Compass, 2016. http://scholarscompass.vcu.edu/etd/4470.

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This paper is a study on some upper bounds of the Mertens function, which is often considered somewhat of a ``mysterious" function in mathematics and is closely related to the Riemann Hypothesis. We discuss some known bounds of the Mertens function, and also seek new bounds with the help of an automated conjecture-making program named CONJECTURING, which was created by C. Larson and N. Van Cleemput, and inspired by Fajtowicz's Dalmatian Heuristic. By utilizing this powerful program, we were able to form, validate, and disprove hypotheses regarding the Mertens function and how it is bounded.
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Alcántara, Bode Julio. "A conjecture about the non-trivial zeroes of the Riemann zeta function." Pontificia Universidad Católica del Perú, 2014. http://repositorio.pucp.edu.pe/index/handle/123456789/97185.

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Some heuristic arguments are given in support of the following conjecture: If the Riemann Hypothesis (RH) does not hold then the number of zeroes of the Riemann zeta function with real part σ >  ½ is infinite.
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Ranorovelonalohotsy, Marie Brilland Yann. "Riemann hypothesis for the zeta function of a function field over a finite field." Thesis, Stellenbosch : Stellenbosch University, 2013. http://hdl.handle.net/10019.1/85713.

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Lucas, Fábio Rodrigues. "Polinômios e funções inteiras com zeros reais." [s.n.], 2010. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306953.

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Orientador: Dimitar Kolev Dimitrov<br>Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica<br>Made available in DSpace on 2018-08-16T01:35:19Z (GMT). No. of bitstreams: 1 Lucas_FabioRodrigues_D.pdf: 837192 bytes, checksum: 1cec40a06f620203e95cbca6134fd41a (MD5) Previous issue date: 2010<br>Resumo: Nesta tese abordamos alguns problemas relacionados com zeros de polinômios e de funções inteiras. Estabelecemos fórmulas explícitas para os polinômios da sequência de Sturm, gerada por um polinômio e pela sua derivada. Como consequência,
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Books on the topic "Riemann hypothesis"

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Borwein, Peter, Stephen Choi, Brendan Rooney, and Andrea Weirathmueller, eds. The Riemann Hypothesis. Springer New York, 2008. http://dx.doi.org/10.1007/978-0-387-72126-2.

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Gilbert, Samuel W. The Riemann hypothesis and the roots of the Riemann Zeta Function. BookSurge Publishing, 2009.

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Chowla, S. The Riemann hypothesis and Hilbert's tenth problem. Gordon and Breach, 1987.

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Spalk, Henrik Gadegaard. Curves, function fields and the Riemann hypothesis. University of Aarhus, Dept. of Mathematics, 2001.

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Dijk, Gerrit van, and Masato Wakayama, eds. Casimir Force, Casimir Operators and the Riemann Hypothesis. DE GRUYTER, 2010. http://dx.doi.org/10.1515/9783110226133.

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Roquette, Peter. The Riemann Hypothesis in Characteristic p in Historical Perspective. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-99067-5.

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Sabbagh, Karl. The Riemann hypothesis: The greatest unsolved problem in mathematics. Farrar, Straus, and Giroux, 2002.

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B, Borwein Peter, ed. The Riemann hypothesis: A resource for the afficionado and virtuoso alike. Springer, 2008.

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Sabbagh, Karl. Dr. Riemann's zeroes. Atlantic, 2002.

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Sabbagh, Karl. Dr. Riemann's zeros: [the search for the $1 million solution to the greatest problem in mathematics]. Atlantic Books, 2003.

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Book chapters on the topic "Riemann hypothesis"

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Beals, Richard, and Roderick S. C. Wong. "The Riemann hypothesis." In Explorations in Complex Functions. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-54533-8_13.

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Vince, John. "The Riemann Hypothesis." In Foundation Mathematics for Computer Science. Springer International Publishing, 2024. http://dx.doi.org/10.1007/978-3-031-66549-3_17.

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Borwein, Peter, Stephen Choi, Brendan Rooney, and Andrea Weirathmueller. "Extensions of the Riemann Hypothesis." In CMS Books in Mathematics. Springer New York, 2008. http://dx.doi.org/10.1007/978-0-387-72126-2_6.

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Maurin, Krzysztof. "Sectional Curvature. Spaces of Constant Curvature. Weyl Hypothesis." In The Riemann Legacy. Springer Netherlands, 1997. http://dx.doi.org/10.1007/978-94-015-8939-0_2.

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Joyner, David, and Jon-Lark Kim. "The Riemann Hypothesis and Coding Theory." In Selected Unsolved Problems in Coding Theory. Birkhäuser Boston, 2011. http://dx.doi.org/10.1007/978-0-8176-8256-9_4.

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Fried, Michael D., and Moshe Jarden. "The Riemann Hypothesis for Function Fields." In Field Arithmetic. Springer Berlin Heidelberg, 1986. http://dx.doi.org/10.1007/978-3-662-07216-5_3.

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Vince, John. "Complex Numbers and the Riemann Hypothesis." In Imaginary Mathematics for Computer Science. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-94637-5_12.

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Lorenzini, Dino. "Frobenius morphisms and the Riemann hypothesis." In Graduate Studies in Mathematics. American Mathematical Society, 1996. http://dx.doi.org/10.1090/gsm/009/11.

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Fried, Michael D., and Moshe Jarden. "The Riemann Hypothesis for Function Fields." In Field Arithmetic. Springer Nature Switzerland, 2023. http://dx.doi.org/10.1007/978-3-031-28020-7_5.

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Tschaffon, Michael E. N., Iva Tkáčová, Helmut Maier, and Wolfgang P. Schleich. "A Primer on the Riemann Hypothesis." In Sketches of Physics. Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-031-32469-7_7.

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Conference papers on the topic "Riemann hypothesis"

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Durmagambetov, A. A. "The solution of the Riemann hypothesis." In APPLIED MATHEMATICS AND COMPUTER SCIENCE: Proceedings of the 1st International Conference on Applied Mathematics and Computer Science. Author(s), 2017. http://dx.doi.org/10.1063/1.4981970.

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Cisło, J., M. Wolf, Piotr Kielanowski, Anatol Odzijewicz, Martin Schlichenmaier, and Theodore Voronov. "Criteria equivalent to the Riemann Hypothesis." In GEOMETRIC METHODS IN PHYSICS. AIP, 2008. http://dx.doi.org/10.1063/1.3043867.

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Huang, M.-D. A. "Riemann hypothesis and finding roots over finite fields." In the seventeenth annual ACM symposium. ACM Press, 1985. http://dx.doi.org/10.1145/22145.22159.

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Schleich, Wolfgang P. "Factorisation of Numbers, Schrödinger Cats and the Riemann Hypothesis." In Frontiers in Optics. OSA, 2008. http://dx.doi.org/10.1364/fio.2008.stha2.

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Planat, Michel. "A physical basis to Riemann hypothesis 1/f frequency noise." In Third international conference on computing anticipatory systems (CASYS'99). AIP, 2000. http://dx.doi.org/10.1063/1.1291289.

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Buchmann, Johannes, and Victor Shoup. "Constructing nonresidues in finite fields and the extended Riemann hypothesis." In the twenty-third annual ACM symposium. ACM Press, 1991. http://dx.doi.org/10.1145/103418.103433.

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Shang, Enlong. "MSoln-PSO: Searching for Multiple Solutions and Numerically Verifying the Riemann Hypothesis." In 2024 7th International Conference on Advanced Algorithms and Control Engineering (ICAACE). IEEE, 2024. http://dx.doi.org/10.1109/icaace61206.2024.10548217.

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Collins, Nick. "Sonification of the Riemann Zeta Function." In ICAD 2019: The 25th International Conference on Auditory Display. Department of Computer and Information Sciences, Northumbria University, 2019. http://dx.doi.org/10.21785/icad2019.003.

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The Riemann zeta function is one of the great wonders of mathematics, with a deep and still not fully solved connection to the prime numbers. It is defined via an infinite sum analogous to Fourier additive synthesis, and can be calculated in various ways. It was Riemann who extended the consideration of the series to complex number arguments, and the famous Riemann hypothesis states that the non-trivial zeroes of the function all occur on the critical line 0:5 + ti, and what is more, hold a deep correspondence with the prime numbers. For the purposes of sonification, the rich set of mathematic
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Grigoriev, Dima Yu, Marek Karpinski, and Andrew M. Odlyzko. "Existence of short proofs for nondivisibility of sparse polynomials under the extended Riemann hypothesis." In Papers from the international symposium. ACM Press, 1992. http://dx.doi.org/10.1145/143242.143287.

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Sohrab, Siavash. "On a Scale Invariant Model of Statistical Mechanics, Kinetic Theory of Ideal Gas, and Riemann Hypothesis." In 50th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition. American Institute of Aeronautics and Astronautics, 2012. http://dx.doi.org/10.2514/6.2012-467.

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