On a positivity property of the Riemann ξ-function

• Autorzy: Jeffrey C. Lagarias
• Języki publikacji: EN

Kategorie tematyczne

• 11R42: Zeta functions and L -functions of number fields
• 11M26: Nonreal zeros of ζ ( s ) and L ( s , χ ) ; Riemann and other hypotheses

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1999
• Tom: 89
• Numer: 3
• Strony: 217-234

Daty

wydano

1999

otrzymano

1998-06-23

poprawiono

1998-11-04

Twórcy

autor

Jeffrey C. Lagarias

• AT&T Labs - Research, Florham Park, New Jersey 07932-0971, U.S.A.

Bibliografia

• [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.
• [2] W. F. Donoghue, Jr., Monotone Matrix Functions and Analytic Continuation, Springer, New York, 1974.
• [3] A. Erdélyi, W. Magnus, F. Oberhettinger and R. G. Tricomi, Higher Transcendental Functions, Vol. I, McGraw-Hill, New York, 1953.
• [4] A. Hinkkanen, On functions of bounded type, Complex Variables Theory Appl. 34 (1997), 119-139.
• [5] N. M. Katz and P. Sarnak, Zeros of zeta functions and symmetry, Bull. Amer. Math. Soc. 36 (1999), 1-26.
• [6] A. Knauf, On a ferromagnetic spin chain, Comm. Math. Phys. 153 (1993), 77-115.
• [7] N. Levinson and H. L. Montgomery, Zeros of the derivatives of the Riemann zeta-function, Acta Math. 133 (1974), 397-413.
• [8] S. J. Patterson, An Introduction to the Theory of the Riemann Zeta Function, Cambridge Univ. Press, Cambridge, 1988.
• [9] E. C. Titchmarsh, The Theory of the Riemann Zeta Function, 2nd ed., revised by D. R. Heath-Brown, Oxford Univ. Press, 1986.
• [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.