On q-analogues of Riemann's zeta function
- I. Cherednik
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In the paper, we introduce q-deformations of the Riemann zeta function, extend them to the whole complex plane, establish a q-counterpart of the TlogT-formula for the number of zeros, and discuss theoretically and (mainly) numerically a q-variant of the Riemann hypothesis. The construction is closely related to the recent difference generalization of the Harish-Chandra theory of zonal spherical functions. The q-zeta functions do not satisfy the functional equation but have some analytic advantages.
- On q-analogues of Riemann's zeta function
Volume 7, Issue 4 , pp 447-491
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- Birkhäuser Verlag
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- Key words. Zeta function, Q-gamma function, orthogonal polynomials.
- I. Cherednik (A1)
- Author Affiliations
- A1. Department of Mathematics, University of North Carolina, Chapel Hill, NC 27599-3250, USA,¶ e-mail: firstname.lastname@example.org, US