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Books on the topic 'Rieman's Zeta Function'

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

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1

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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2

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

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3

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

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4

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

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5

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

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6

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

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7

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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8

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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9

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

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10

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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11

Coates, John, A. Raghuram, Anupam Saikia, and R. Sujatha, eds. The Bloch–Kato Conjecture for the Riemann Zeta Function. Cambridge: Cambridge University Press, 2015. http://dx.doi.org/10.1017/cbo9781316163757.

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12

An introduction to the theory of the Riemann zeta-function. Cambridge: Cambridge University Press, 1988.

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13

1972-, Rivoal T., ed. Hypergéométrie et fonction zêta de Riemann. Providence, RI: American Mathematical Society, 2007.

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14

R, Balasubramanian, R. Balasubramanian, and K. Srinivas. The Riemann zeta function and related themes: Papers in honour of Professor K. Ramachandra. Edited by Ramachandra K and Ramanujan Mathematical Society. Mysore: Ramanujan Mathematical Society, 2006.

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15

Ramachandra, K. Lectures on the mean-value and omega-theorems for the Riemann zeta-function. Berlin: Springer-Verlag, 1995.

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16

He, Christina Q. Generalized Minkowski content, spectrum of fractal drums, fractal strings, and the Riemann-zeta-function. Providence, R.I: American Mathematical Society, 1997.

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17

PISRS 2011 International Conference on Analysis, Fractal Geometry, Dynamical Systems and Economics (2011 Messina, Italy). Fractal geometry and dynamical systems in pure and applied mathematics. Edited by Carfi David 1971-, Lapidus, Michel L. (Michel Laurent), 1956-, Pearse, Erin P. J., 1975-, Van Frankenhuysen Machiel 1967-, and Mandelbrot Benoit B. Providence, Rhode Island: American Mathematical Society, 2013.

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18

Edwards, Harold M. Riemann's Zeta Function. Dover Publications, 2001.

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19

Montgomery, Hugh, Michael Th Rassias, and Ashkan Nikeghbali. Exploring the Riemann Zeta Function: 190 years from Riemann's Birth. Springer, 2018.

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20

Spencer, Thomas. Number theory. Edited by Gernot Akemann, Jinho Baik, and Philippe Di Francesco. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198744191.013.24.

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This article examines some of the connections between random matrix theory (RMT) and number theory, including the modelling of the value distributions of the Riemann zeta function and other L-functions as well as the statistical distribution of their zeros. Number theory has been used in RMT to address seemingly disparate questions, such as modelling mean and extreme values of the Riemann zeta function and counting points on curves. One thing in common among the applications of RMT to number theory is the L-function. The statistics of the critical zeros of these functions are believed to be related to those of the eigenvalues of random matrices. The article first considers the truth of the generalized Riemann hypothesis before discussing the values of the Riemann zeta function, the values of L-functions, and further areas of interest with respect to the connections between RMT and number theory
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21

Ivić, A. The Riemann zeta-function: The theory of the Riemann zeta-function with applications. Wiley, 1985.

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22

(Translator), Neal Koblitz, ed. The Riemann Zeta-Function (De Gruyter Expositions in Mathematics). Walter de Gruyter, 1992.

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23

The Riemann Zeta-Function: Theory and Applications. Dover Publications, 2003.

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24

Spectral Theory of the Riemann Zeta-Function. Cambridge University Press, 2008.

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25

Laurincikas, Antanas. Limit Theorems for the Riemann Zeta-Function. Laurincikas Antanas, 2010.

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26

Bloch-Kato Conjecture for the Riemann Zeta Function. Cambridge University Press, 2015.

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27

Patterson, S. J. An Introduction to the Theory of the Riemann Zeta-Function (Cambridge Studies in Advanced Mathematics). Cambridge University Press, 1995.

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28

Keating, Jon P. Random matrices and number theory: some recent themes. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198797319.003.0008.

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The aim of this chapter is to motivate and describe some recent developments concerning the applications of random matrix theory to problems in number theory. The first section provides a brief and rather selective introduction to the theory of the Riemann zeta function, in particular to those parts needed to understand the connections with random matrix theory. The second section focuses on the value distribution of the zeta function on its critical line, specifically on recent progress in understanding the extreme value statistics gained through a conjectural link to log–correlated Gaussian random fields and the statistical mechanics of glasses. The third section outlines some number-theoretic problems that can be resolved in function fields using random matrix methods. In this latter case, random matrix theory provides the only route we currently have for calculating certain important arithmetic statistics rigorously and unconditionally.
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29

Ivic, Aleksandar. Lectures on Mean Values of the Riemann Zeta Function (Tata Institute Lectures on Mathematics & Physics). Springer-Verlag Berlin and Heidelberg GmbH & Co. K, 1992.

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30

Ramachandra, K. Lectures on the Mean-Value and Omega Theorems for the Riemann Zeta-Function (Lectures on Mathematics and Physics). Springer, 1996.

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31

Ivic, A. Lectures on Mean Values of the Riemann Zeta Function: Lectures (Tata Institute of Fundamental Research Lectures on Mathemati). Springer, 1993.

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32

In Search of the Riemann Zeros: Strings, Fractal Membranes and Noncommutative Spacetimes. Amer Mathematical Society, 2008.

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33

Bohr-Jessen Limit Theorem, Revisited. Tokyo, Japan: Mathematical Society of Japan, 2014.

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