Relevant bibliographies by topics / Rieman's Zeta Function

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

Academic literature on the topic 'Rieman's Zeta Function'

Author: Grafiati
Published: 4 June 2021
Last updated: 13 February 2022

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Journal articles on the topic "Rieman's Zeta Function"

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Garunkštis, Ramūnas, and Joern Steuding. "QUESTIONS AROUND THE NONTRIVIAL ZEROS OF THE RIEMANN ZETA-FUNCTION. COMPUTATIONS AND CLASSIFICATIONS." Mathematical Modelling and Analysis 16, no. 1 (April 8, 2011): 72–81. http://dx.doi.org/10.3846/13926292.2011.560616.

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We study the sequence of nontrivial zeros of the Riemann zeta-function with respect to sequences of zeros of other related functions, namely, the Hurwitz zeta-function and the derivative of Riemann's zeta-function. Finally, we investigate connections of the nontrivial zeros with the periodic zeta-function. On the basis of computation we derive several classifications of the nontrivial zeros of the Riemann zeta-function and stateproblems which mightbe ofinterestfor abetter understanding of the distribution of those zeros.
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RODGERS, BRAD. "A CENTRAL LIMIT THEOREM FOR THE ZEROES OF THE ZETA FUNCTION." International Journal of Number Theory 10, no. 02 (February 20, 2014): 483–511. http://dx.doi.org/10.1142/s1793042113501054.

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On the assumption of the Riemann hypothesis, we generalize a central limit theorem of Fujii regarding the number of zeroes of Riemann's zeta function that lie in a mesoscopic interval. The result mirrors results of Spohn and Soshnikov and others in random matrix theory. In an appendix we put forward some general theorems regarding our knowledge of the zeta zeroes in the mesoscopic regime.
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TSUMURA, HIROFUMI. "On functional relations between the Mordell–Tornheim double zeta functions and the Riemann zeta function." Mathematical Proceedings of the Cambridge Philosophical Society 142, no. 3 (May 2007): 395–405. http://dx.doi.org/10.1017/s0305004107000059.

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AbstractIn this paper, we give certain analytic functional relations between the Mordell–Tornheim double zeta functions and the Riemann zeta function. These can be regarded as continuous generalizations of the known discrete relations between the Mordell–Tornheim double zeta values and the Riemann zeta values at positive integers discovered in the 1950's.
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Bump, Daniel, and Eugene K. S. Ng. "On Riemann's zeta function." Mathematische Zeitschrift 192, no. 2 (June 1986): 195–204. http://dx.doi.org/10.1007/bf01179422.

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Laurinčikas, Antanas, and Renata Macaitienė˙. "Joint universality of the Riemann zeta-function and Lerch zeta-functions." Nonlinear Analysis: Modelling and Control 18, no. 3 (July 25, 2013): 314–26. http://dx.doi.org/10.15388/na.18.3.14012.

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In the paper, we prove a joint universality theorem for the Riemann zeta-function and a collection of Lerch zeta-functions with parameters algebraically independent over the field of rational numbers.
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Moser, Jan. "On the distribution of multiplicities of zeros of Riemann zeta function." Czechoslovak Mathematical Journal 44, no. 3 (1994): 385–404. http://dx.doi.org/10.21136/cmj.1994.128478.

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Acedo, Luis. "On an Exact Relation between ζ″(2) and the Meijer G -Functions." Mathematics 7, no. 4 (April 24, 2019): 371. http://dx.doi.org/10.3390/math7040371.

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In this paper we consider some integral representations for the evaluation of the coefficients of the Taylor series for the Riemann zeta function about a point in the complex half-plane ℜ ( s ) > 1 . Using the standard approach based upon the Euler-MacLaurin summation, we can write these coefficients as Γ ( n + 1 ) plus a relatively smaller contribution, ξ n . The dominant part yields the well-known Riemann’s zeta pole at s = 1 . We discuss some recurrence relations that can be proved from this standard approach in order to evaluate ζ ″ ( 2 ) in terms of the Euler and Glaisher-Kinkelin constants and the Meijer G -functions.
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Gelbart, Stephen S., and Stephen D. Miller. "Riemann's zeta function and beyond." Bulletin of the American Mathematical Society 41, no. 01 (October 30, 2003): 59–113. http://dx.doi.org/10.1090/s0273-0979-03-00995-9.

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AREF'EVA, I. YA, and I. V. VOLOVICH. "QUANTIZATION OF THE RIEMANN ZETA-FUNCTION AND COSMOLOGY." International Journal of Geometric Methods in Modern Physics 04, no. 05 (August 2007): 881–95. http://dx.doi.org/10.1142/s021988780700234x.

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Quantization of the Riemann zeta-function is proposed. We treat the Riemann zeta-function as a symbol of a pseudodifferential operator and study the corresponding classical and quantum field theories. This approach is motivated by the theory of p-adic strings and by recent works on stringy cosmological models. We show that the Lagrangian for the zeta-function field is equivalent to the sum of the Klein–Gordon Lagrangians with masses defined by the zeros of the Riemann zeta-function. Quantization of the mathematics of Fermat–Wiles and the Langlands program is indicated. The Beilinson conjectures on the values of L-functions of motives are interpreted as dealing with the cosmological constant problem. Possible cosmological applications of the zeta-function field theory are discussed.
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Noda, Takumi. "Some generating functions of the Riemann zeta function." Banach Center Publications 118 (2019): 107–11. http://dx.doi.org/10.4064/bc118-6.

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Dissertations / Theses on the topic "Rieman's Zeta Function"

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Dauguet, Simon. "Généralisations du critère d’indépendance linéaire de Nesterenko." Thesis, Paris 11, 2014. http://www.theses.fr/2014PA112085/document.

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Cette thèse s'inscrit dans le prolongement du résultat d'Apéry donnant l'irrationalité de ζ (3) et de celui de Ball-Rivoal prouvant qu'il existe une infinité d'entiers impairs en lesquels la fonction zêta de Riemann prend des valeurs irrationnelles. Un outil crucial dans la démonstration de Ball-Rivoal est le critère d'indépendance linéaire de Nesterenko, qui a été généralisé par Fischler et Zudilin pour exploiter sous des hypothèses très restrictives la présence de diviseurs communs aux coefficients des formes linéaires. Une généralisation ultérieure due à Fischler s'applique lorsqu'on dispose d'approximations simultanées des nombres réels en question (et non plus de combinaisons Z-linéaires petites de ces nombres).Dans cette thèse, on améliore ce dernier résultat en affaiblissant considérablement les hypothèses sur les diviseurs. On démontre aussi un critère d'indépendance linéaire analogue, dans l'esprit de celui de Siegel. Dans une autre partie en commun avec Zudilin, on construit, en utilisant des identités hypergéométriques, des approximations simultanées de ζ (2) et ζ (3) qui permettent de démontrer en même temps l'irrationalité de ces deux nombres. En appliquant essentiellement le critère démontré précédemment, on en déduit une minoration des combinaisons Z-linéaires de 1, ζ 2) et ζ (3), sous des hypothèses de divisibilité très fortes sur les coefficients (si bien que l'indépendance linéaire sur Q de ces trois nombres est toujours conjecturale)
This Ph.D. thesis lies in the path opened by Apéry who proved the irrationality of ζ(3) andalready followed by Ball-Rivoal who proved that there are infinitely many odd integers at which Riemann zeta function takes irrational values. A fundamental tool in the proof of Ball-Rivoal is Nesterenko’s linear independence criterion. This criterion has been generalized by Fischler and Zudilin to use common divisors of the coefficients of linear forms, under some restrictive assumptions. Then Fischler gave another generalization for simultaneous approximations (instead of small Z-linear combinations).In this Ph.D. thesis, we improve this last result by greatly weakening the assumption on thedivisors. We prove also an analogous linear independence criterion in the spirit of Siegel. Inanother part joint with Zudilin, we construct simultaneous linear approximations to ζ(2) and ζ(3) using hypergeometric identitites. These linear approximations allow one to prove at thesame time the irrationality of ζ(2) and that of ζ(3). Then, using a criterion from the previouspart, we deduce a lower bound on Z-linear combinations of 1, ζ(2) and ζ(3), under somestrong divisibility hypotheses on the coefficients (so that the Q-linear independence of thesethree numbers still remains an open problem)
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Kalpokas, Justas. "Discrete moments of the Riemann zeta function and Dirichlet L-functions." Doctoral thesis, Lithuanian Academic Libraries Network (LABT), 2012. http://vddb.laba.lt/obj/LT-eLABa-0001:E.02~2012~D_20121119_130728-97328.

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In mathematics, analytic number theory is a branch of number theory that uses methods from mathematical analysis to solve problems that concern the integers. It is often said to have begun with Dirichlet's introduction of Dirichlet L-functions. In analytic number theory one of the main investigation objects is the Riemann zeta function. The Riemann hypothesis states that all non-trivial zeros of the Riemann zeta function lie on the critical line. In the thesis we investigate value distribution of the Riemann zeta function on the critical line. To do so we use the curve of the Riemann zeta function on the critical line. A problem connected to the curve asks the question whether the curve is dense in the complex plane. We prove that the curve expands to all directions on the complex plane. A separete case of the main result can be stated as follows Riemann zeta function has infinetly many negative values on the critical line and they are unbounded.
Analizinė skaičių teorija yra skaičių teorijos dalis, kuri, naudodama matematinės analizės ir kompleksinio kintamojo funkcijų tyrimo metodus, sprendžia uždavinius susijusius su sveikaisiais skaičiais. Manoma, kad analizinės skaičių teorijos pradžią žymi Dirichlet eilučių ir Dirichlet L-funkcijų taikymai. Vienas iš pagrindinių analizinės skaičių teorijos tyrimo objektų yra Riemann’o dzeta funkcija. Riemann’o hipotezė teigia, kad visi netrivialieji nuliai yra ant kritinės tiesės. Disertacijoje nagrinėjamas Riemann’o dzeta funckijos reikšmių pasiskirstymas ant kritinės tiesės. Tam pasitelkiama Riemann’o dzeta funkcijos kreivė. Svarbus klausimas susijęs su kreive yra ar ši kreivė yra visur tiršta kompleksinių skaičių plokštumoje. Disertacijoje įrodoma, kad kreivė plečiasi į visas puse kompleksinių skaičių plokštumoje. Atskiras disertacijos pagrindinio rezultato atvejis gali būti formuluojamas taip – Riemann’o dzeta funkcija ant kritinės tiesės įgyja be galo daug neigiamų reikšmių, kurios yra neaprėžtos.
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Reyes, Ernesto Oscar. "The Riemann zeta function." CSUSB ScholarWorks, 2004. https://scholarworks.lib.csusb.edu/etd-project/2648.

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The Riemann Zeta Function has a deep connection with the distribution of primes. This expository thesis will explain the techniques used in proving the properties of the Rieman Zeta Function, its analytic continuation to the complex plane, and the functional equation that the the Riemann Zeta Function satisfies.
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Merrill, Katherine J. "Ramanujan's Formula for the Riemann Zeta Function Extended to L-Functions." Fogler Library, University of Maine, 2005. http://www.library.umaine.edu/theses/pdf/MerrillKJ2005.pdf.

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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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Šimėnas, Raivydas. "Riemann'o hipotezės Speiser'io ekvivalentas." Master's thesis, Lithuanian Academic Libraries Network (LABT), 2014. http://vddb.library.lt/obj/LT-eLABa-0001:E.02~2012~D_20140704_171541-67476.

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A. Speiser'is parodė, kad Riemann'o hipotezė yra ekvivalenti tam, kad Riemann'o dzeta funkcijos išvestinė neturi netrivialių nulių į kairę nuo kritinės tiesės. Kiekybinis šio fakto rezultatas buvo pasiektas N. Levinsono ir H. Montgomerio. Šie rezultatai buvo apibendrinti daugeliui dzeta funkcijų, kurioms tikimasi, kad Riemann'o hipotezė galioja. Šiame darbe mes apibendriname Speiser'io ekvivalentą dzeta-funkcijoms. Mes tiriame sąryšį tarp netrivialių nulių išplėstinės Selbergo klasės funkcijoms ir jų išvestinėms šiame regione. Šiai klasei priklauso ir funkcijos, kurioms Riemann'o hipotezė neteisinga. Kaip pavyzdį, mes skaitiniu būdu tiriame sąryšius tarp Dirichlet L-funkcijų ir jų išvestinių tiesinių kombinacijų.
A. Speiser showed that the Riemann hypothesis is equivalent to the absence of non-trivial zeros of the derivative of the Riemann zeta-function left of the critical line. The quantitative version of this result was obtained by N. Levinson and H. Montgomery. This result (or the quantitative version of this result proved by N. Levinson and H. Montgomery) were generalized for many zeta-functions for which the Riemann hypothesis is expected. Here we generalize the Speiser equivalent for zeta-functions. We also investigate the relationship between the on-trivial zeros of the extended Selberg class functions and of their derivatives in this region. This class contains zeta functions for which Riemann hypothesis is not true. As an example, we study the relationship between the trajectories of zeros of linear combinations of Dirichlet $L$-functions and of their derivatives computationally.
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Tsumura, Hirofumi, and Kohji Matsumoto. "On Witten multiple zeta-functions associated with semisimple Lie algebras I." Annales de L'Institut Fourier, 2006. http://hdl.handle.net/2237/20336.

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Gauthier, Paul M., and Nikolai Tarkhanov. "A covering property of the Riemann zeta-function." Universität Potsdam, 2004. http://opus.kobv.de/ubp/volltexte/2008/2668/.

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For each compact subset K of the complex plane C which does not surround zero, the Riemann surface Sζ of the Riemann zeta function restricted to the critical half-strip 0 < Rs < 1/2 contains infinitely many schlicht copies of K lying ‘over’ K. If Sζ also contains at least one such copy, for some K which surrounds zero, then the Riemann hypothesis fails.
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Steuding, Jörn. "On simple zeros of the Riemann zeta-function." [S.l. : s.n.], 1999. http://deposit.ddb.de/cgi-bin/dokserv?idn=95589820X.

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Steuding, Rasa, Jörn Steuding, Kohji Matsumoto, Antanas Laurinčikas, and Ramūnas Garunkštis. "Effective uniform approximation by the Riemann zeta-function." Department of Mathematics of the Universitat Autònoma de Barcelona, 2010. http://hdl.handle.net/2237/20429.

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Books on the topic "Rieman's Zeta Function"

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Montgomery, Hugh, Ashkan Nikeghbali, and Michael Th Rassias, eds. Exploring the Riemann Zeta Function. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-59969-4.

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The Riemann zeta-function: The theory of the Riemann zeta-function with applications. New York: Wiley, 1985.

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Lectures on the Riemann zeta function. Providence, Rhode Island: American Mathematical Society, 2014.

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Motohashi, Y. Spectral theory of the Riemann zeta-function. Cambridge: Cambridge University Press, 1997.

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Laurinčikas, Antanas. Limit theorems for the Riemann zeta-function. Dordrecht: Kluwer Academic, 1996.

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R, Heath-Brown D., ed. The theory of the Riemann zeta-function. 2nd ed. Oxford [Oxfordshire]: Clarendon Press, 1986.

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Laurinčikas, Antanas. Limit Theorems for the Riemann Zeta-Function. Dordrecht: Springer Netherlands, 1996. http://dx.doi.org/10.1007/978-94-017-2091-5.

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Ivić, A. Lectures on mean values of the Riemann Zeta function. Berlin: Published for the Tata Institute of Fundamental Research [by] Springer-Vlg., 1991.

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Gilbert, Samuel W. The Riemann hypothesis and the roots of the Riemann Zeta Function. [Charleston, S.C.]: BookSurge Publishing, 2009.

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Ivic, A. Lectures on mean values of the Riemann zeta function. Berlin: Springer-Verlag for theTata Institute of Fundamental Research, 1991.

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Book chapters on the topic "Rieman's Zeta Function"

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Rivat, Joël. "Riemann’s Zeta Function." In Lecture Notes in Mathematics, 27–52. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-74908-2_5.

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Schweizer, Wolfgang. "Riemann Zeta Function." In Special Functions in Physics with MATLAB, 233–36. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-64232-7_20.

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Dittrich, Walter. "Riemann’s Zeta Function Regularization." In SpringerBriefs in History of Science and Technology, 39–43. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-61049-4_8.

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Dittrich, Walter. "Riemann’s Zeta Function Regularization." In SpringerBriefs in History of Science and Technology, 39–43. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-91482-4_8.

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Beals, Richard, and Roderick S. C. Wong. "The Riemann zeta function." In Explorations in Complex Functions, 155–65. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-54533-8_11.

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Tenenbaum, Gérald, and Michel Mendès France. "The Riemann zeta function." In The Student Mathematical Library, 29–49. Providence, Rhode Island: American Mathematical Society, 2000. http://dx.doi.org/10.1090/stml/006/02.

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Wagon, Stan. "The Riemann Zeta Function." In Mathematica® in Action, 539–54. New York, NY: Springer New York, 1999. http://dx.doi.org/10.1007/978-1-4612-1454-0_26.

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Wagon, Stan. "The Riemann Zeta Function." In Mathematica in Action, 505–22. New York, NY: Springer New York, 2010. http://dx.doi.org/10.1007/978-0-387-75477-2_21.

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Agarwal, Ravi P., Kanishka Perera, and Sandra Pinelas. "The Riemann Zeta Function." In An Introduction to Complex Analysis, 303–7. Boston, MA: Springer US, 2011. http://dx.doi.org/10.1007/978-1-4614-0195-7_46.

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Rassias, Michael Th. "The Riemann zeta function." In Problem-Solving and Selected Topics in Number Theory, 83–98. New York, NY: Springer New York, 2010. http://dx.doi.org/10.1007/978-1-4419-0495-9_7.

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Conference papers on the topic "Rieman's Zeta Function"

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Collins, Nick. "Sonification of the Riemann Zeta Function." In ICAD 2019: The 25th International Conference on Auditory Display. Newcastle upon Tyne, United Kingdom: 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 mathematical ideas to analyse the zeta function provide strong resources for sonic experimentation. The positions of the zeroes on the critical line can be directly sonified, as can values of the zeta function in the complex plane, approximations to the prime spectrum of prime powers and the Riemann spectrum of the zeroes rendered; more abstract ideas concerning the function also provide interesting scope.
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Xavier, G. Britto Antony, T. Sathinathan, and D. Arun. "Fractional order Riemann zeta factorial function." In SECOND INTERNATIONAL CONFERENCE OF MATHEMATICS (SICME2019). Author(s), 2019. http://dx.doi.org/10.1063/1.5097535.

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Joffily, Sérgio. "The Riemann Zeta Function and Vacuum Spectrum." In Fourth International Winter Conference on Mathematical Methods in Physics. Trieste, Italy: Sissa Medialab, 2004. http://dx.doi.org/10.22323/1.013.0026.

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Sulaiman, W. T., Theodore E. Simos, George Psihoyios, Ch Tsitouras, and Zacharias Anastassi. "Turan Inequalites for the Riemann Zeta Functions." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2011: International Conference on Numerical Analysis and Applied Mathematics. AIP, 2011. http://dx.doi.org/10.1063/1.3636956.

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Guariglia, Emanuel, and Sergei Silvestrov. "A functional equation for the Riemann zeta fractional derivative." In ICNPAA 2016 WORLD CONGRESS: 11th International Conference on Mathematical Problems in Engineering, Aerospace and Sciences. Author(s), 2017. http://dx.doi.org/10.1063/1.4972655.

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Guariglia, Emanuel, and Sergei Silvestrov. "A functional equation for the Riemann Zeta fractional derivative." In ICNPAA 2016 WORLD CONGRESS: 11th International Conference on Mathematical Problems in Engineering, Aerospace and Sciences. Author(s), 2017. http://dx.doi.org/10.1063/1.4972738.

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PARIS, R. B. "NEW ASYMPTOTIC FORMULAS FOR THE RIEMANN ZETA FUNCTION ON THE CRITICAL LINE." In Proceedings of the International Workshop. WORLD SCIENTIFIC, 2000. http://dx.doi.org/10.1142/9789812792303_0020.

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Tihanyi, Norbert. "Fast Method for Locating Peak Values of the Riemann Zeta Function on the Critical Line." In 2014 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC). IEEE, 2014. http://dx.doi.org/10.1109/synasc.2014.20.

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Quintana Murillo, Joaqui´n, and Santos Bravo Yuste. "On an Explicit Difference Method for Fractional Diffusion and Diffusion-Wave Equations." In ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2009. http://dx.doi.org/10.1115/detc2009-86625.

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An explicit difference scheme for solving fractional diffusion and fractional diffusion-wave equations, in which the fractional derivative is in the Caputo form, is considered. The two equations are studied separately: for the fractional diffusion equation, the L1 discretization formula is employed, whereas the L2 discretization formula is used for the fractional diffusion-wave equation. Its accuracy is similar to other well-known explicit difference schemes, but its region of stability is larger. The stability analysis is carried out by means of a procedure similar to the standard von Neumann method. The stability bound, which is given in terms of the the Riemann Zeta function, is checked numerically.
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