## Functiones et Approximatio Commentarii Mathematici

### A note on the gaps between zeros of Epstein's zeta-functions on the critical line

#### Abstract

It is proved that Epstein's zeta-function $\zeta_{Q}(s)$, related to a positive definite integral binary quadratic form, has a zero $1/2 + i\gamma$ with $T \leq \gamma \leq T + T^{{3/7} +\varepsilon}$ for sufficiently large positive numbers $T$. This is an improvement of the result by M. Jutila and K. Srinivas (Bull. London Math. Soc. 37 (2005) 45--53).

#### Article information

Source
Funct. Approx. Comment. Math., Volume 57, Number 2 (2017), 235-253.

Dates
First available in Project Euclid: 28 March 2017

https://projecteuclid.org/euclid.facm/1490688026

Digital Object Identifier
doi:10.7169/facm/1630

Mathematical Reviews number (MathSciNet)
MR3732897

Zentralblatt MATH identifier
06864173

#### Citation

Baier, Stephan; Kotyada, Srinivas; Sangale, Usha Keshav. A note on the gaps between zeros of Epstein's zeta-functions on the critical line. Funct. Approx. Comment. Math. 57 (2017), no. 2, 235--253. doi:10.7169/facm/1630. https://projecteuclid.org/euclid.facm/1490688026

#### References

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