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ON THE ABSENCE OF ZEROS IN INFINITE ARITHMETIC PROGRESSION FOR CERTAIN ZETA FUNCTIONS

  • TEERAPAT SRICHAN (a1)

Abstract

Putnam [‘On the non-periodicity of the zeros of the Riemann zeta-function’, Amer. J. Math.76 (1954), 97–99] proved that the sequence of consecutive positive zeros of $\unicode[STIX]{x1D701}(\frac{1}{2}+it)$ does not contain any infinite arithmetic progression. We extend this result to a certain class of zeta functions.

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This work was supported by the Thailand Research Fund (MRG6080210).

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[1] Lapidus, M. L. and van Frankenhuijsen, M., Fractal Geometry, Complex Dimensions and Zeta Functions (Springer, New York, 2006).
[2] Li, X. and Radziwiłł, M., ‘The Riemann zeta function on vertical arithmetic progressions’, Int. Math. Res. Not. 2015(2) (2015), 325354.
[3] Putnam, C. R., ‘On the non-periodicity of the zeros of the Riemann zeta-function’, Amer. J. Math. 76 (1954), 9799.
[4] Titchmarch, E. C., The Riemann Zeta-Function, 2nd edn (Oxford University Press, Oxford, 1986).
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ON THE ABSENCE OF ZEROS IN INFINITE ARITHMETIC PROGRESSION FOR CERTAIN ZETA FUNCTIONS

  • TEERAPAT SRICHAN (a1)

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