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Riemann Zeta Function

We prove that the unique shift ε = φ − 1 — where φ = (1 + √5)/2 is the Golden Ratio — makes the 2-regularized Fredholm determinant of the diagonal operator Aₛ+ε on ℓ²(primes) equal (up to an entire, nowhere-vanishing factor) to ζ(s)⁻¹. Explicitly,     det₂(I − Aₛ+φ−1 · E_φ(s)) = ζ(s)⁻¹, for Re s > ½,   where E_φ is an elementary exponential built ...
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The Riemann Zeta-Function

Nature, 1952
The Theory of the Riemann Zeta-Function By Prof. E. C. Titchmarsh. Pp. vii + 346. (Oxford: Clarendon Press; London: Oxford University Press, 1951.) 40s. net.
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The Riemann Zeta Function

2011
The Riemann zeta function is one of the most important functions of classical mathematics, with a variety of applications in analytic number theory. In this lecture, we shall study some of its elementary properties.
Ravi P. Agarwal, Kanishka Perera, Sandra Pinelas   +2 more
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The Riemann Zeta Function

1998
In order to make progress in number theory, it is sometimes necessary to use techniques from other areas of mathematics, such as algebra, analysis or geometry. In this chapter we give some number-theoretic applications of the theory of infinite series.
Gareth A. Jones, J. Mary Jones
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Riemann’s Zeta Function Regularization

2018
In this final section, we want to introduce the concept of the zeta function in connection with regularizing certain problems in quantum physics where infinities occur.
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The Riemann zeta function

2001
Abstract The theory we presented in Chapter 10 works globally over the adeles by simply taking the product of the local theories for p  ≥  η .
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The Riemann Zeta Function

1999
The surface is a graph of the reciprocal of the absolute value of the Riemann zeta function ζ (s). The spikes correspond to the zeros on the critical line ½ + iy. Recall that the global behavior of π(x), the prime distribution function, is well approximated by Riemann’s smooth function R(x) (discussed in Chapter 2). More delicate information about π(x),
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ON THE RIEMANN ZETA FUNCTION

The Quarterly Journal of Mathematics, 1945
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On the Riemann Zeta Function

Journal of the London Mathematical Society, 1969
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The Riemann Zeta Function

2005
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