On a positivity property of the Riemann ξ-function

Jeffrey C. Lagarias

Acta Arithmetica (1999)

  • Volume: 89, Issue: 3, page 217-234
  • ISSN: 0065-1036

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Jeffrey C. Lagarias. "On a positivity property of the Riemann ξ-function." Acta Arithmetica 89.3 (1999): 217-234. <http://eudml.org/doc/207266>.

@article{JeffreyC1999,
author = {Jeffrey C. Lagarias},
journal = {Acta Arithmetica},
keywords = {Riemann zeta-function; Dedekind zeta-function; Mittag-Leffler expansion; algebraic number field},
language = {eng},
number = {3},
pages = {217-234},
title = {On a positivity property of the Riemann ξ-function},
url = {http://eudml.org/doc/207266},
volume = {89},
year = {1999},
}

TY - JOUR
AU - Jeffrey C. Lagarias
TI - On a positivity property of the Riemann ξ-function
JO - Acta Arithmetica
PY - 1999
VL - 89
IS - 3
SP - 217
EP - 234
LA - eng
KW - Riemann zeta-function; Dedekind zeta-function; Mittag-Leffler expansion; algebraic number field
UR - http://eudml.org/doc/207266
ER -

References

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  1. [1] J.-B. Bost and A. Connes, Hecke algebras, type III factors and phase transitions with spontaneous symmetry breaking in number theory, Selecta Math. 1 (1995), 411-457. Zbl0842.46040
  2. [2] W. F. Donoghue, Jr., Monotone Matrix Functions and Analytic Continuation, Springer, New York, 1974. Zbl0278.30004
  3. [3] A. Erdélyi, W. Magnus, F. Oberhettinger and R. G. Tricomi, Higher Transcendental Functions, Vol. I, McGraw-Hill, New York, 1953. Zbl0051.30303
  4. [4] A. Hinkkanen, On functions of bounded type, Complex Variables Theory Appl. 34 (1997), 119-139. 
  5. [5] N. M. Katz and P. Sarnak, Zeros of zeta functions and symmetry, Bull. Amer. Math. Soc. 36 (1999), 1-26. Zbl0921.11047
  6. [6] A. Knauf, On a ferromagnetic spin chain, Comm. Math. Phys. 153 (1993), 77-115. Zbl0776.11047
  7. [7] N. Levinson and H. L. Montgomery, Zeros of the derivatives of the Riemann zeta-function, Acta Math. 133 (1974), 397-413. Zbl0287.10025
  8. [8] S. J. Patterson, An Introduction to the Theory of the Riemann Zeta Function, Cambridge Univ. Press, Cambridge, 1988. Zbl0641.10029
  9. [9] E. C. Titchmarsh, The Theory of the Riemann Zeta Function, 2nd ed., revised by D. R. Heath-Brown, Oxford Univ. Press, 1986. Zbl0601.10026
  10. [10] A. M. Turing, Some calculations of the Riemann zeta function, Proc. London Math. Soc. 3 (1953), 99-117; also in: Collected Works of A. M. Turing, Vol. I, J. L. Britton (ed.), North-Holland, 1992, 79-97. Notes, 254-261. Zbl0050.08101

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