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

Published online by Cambridge University Press:  15 August 2018

TEERAPAT SRICHAN*
Affiliation:
Department of Mathematics, Faculty of Science, Kasetsart University, Bangkok 10900, Thailand email [email protected]
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Abstract

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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.

Type
Research Article
Copyright
© 2018 Australian Mathematical Publishing Association Inc. 

Footnotes

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

References

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