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[Texts]## 11M: Zeta and L-functions: analytic theory |

- 11M06: zeta(s) and L(s, chi)
- 11M20: Real zeros of L(s, chi); results on L(1, chi)
- 11M26: Nonreal zeros of zeta (s) and L(s, chi); Riemann and other hypotheses
- 11M35: Hurwitz and Lerch zeta functions
- 11M36: Selberg zeta functions and regularized determinants
- 11M38: Zeta and
*L*-functions in characteristic*p*[new in 2000] - 11M41: Other Dirichlet series and zeta functions {For local and global ground fields, see 11R42, 11R52, 11S40, 11S45; for algebro-geometric methods, see 14G10; see also 11E45, 11F66, 11F70, 11F72}
- 11M45: Tauberian theorems, See also 40E05
- 11M99: None of the above but in this section

Parent field: 11: Number Theory

Browse all (old) classifications for this area at the AMS.

This is one of the more commonly-studied areas of number theory. Among the many choices of text:

- Titchmarsh, E.: "Theory of the Riemann zeta-function", Clarendon, Oxford, 1951; second edition, Oxford Univ. Press, New York, 1986; MR 88c:11049
- Ivic, A.: "The Riemann zeta-function", Wiley, New York, 1985; MR 87d:11062
- Vaughan, R. C., "The Hardy-Littlewood method", Cambridge University Press, Cambridge-New York, 1981. 172 pp. ISBN 0-521-23439-5
- Karatsuba, Anatoly A., "Complex analysis in number theory", CRC Press, Boca Raton, FL, 1995. 187 pp. ISBN 0-8493-2866-7

See also the references for number theory in general.

- Dan Bump has a Riemann Hypothesis page.
- L-functions [Brian Conrey]

- Euler and the birth of analytic number theory
- "Proof" of closed formulae for zeta(2n) (e.g. Sum (1/n^2) = pi^2/6 )
- Computing values of the Riemann Zeta function
- Stieltjes' expansion of zeta(s) near s=1
- Images of zeta along vertical lines
- Evaluating zeta and finding zeros
- Locations of zeros of zeta
- A sampling of recent work on the Riemann zeta-function and the Riemann hypothesis
- What's new with the Riemann Hypothesis?
- What is the Generalized Riemann Hypothesis?
- Estimating the number of primes less than N with zeros of the zeta function.
- Connection between zeros of zeta and the error term in the PNT
- Generalizations of the Riemann zeta function: Polygamma function, Hurwitz zeta, etc
- Adamchik's formula for the Hurwitz zeta function
- Dirichlet series related to zeta function and arithmetic functions
- Comments on Jacobi sums (Sum exp( - n(n+a)/2 ). )
- Computing psi(x)=Gamma'(x)/Gamma(x) at rational points.
- Artin's conjecture on zeta functions of number fields.
- Sums and products taken over all primes, involving Dirichlet characters
- Values of certain Dirichlet L-functions
- Inverting a discrete convolution
- (Tauberian) types of convergence of sequences

Last modified 2000/01/19 by Dave Rusin. Mail: