The Epstein–Riemann conjecture for the identity Epstein zeta function
The Epstein–Riemann conjecture for the identity Epstein zeta function
Let , let be the Epstein zeta function associated with a real-valued positive definite matrix , and let denote the case . A critical zero is a zero with . Epstein–Riemann conjecture. All critical zeros of have real part
This extends the Riemann-hypothesis phenomenon to Epstein zeta functions and, via the identity , to the spectral zeta function of a flat torus. The source presents the assertion as a conjecture and gives no resolution status.
Sources & referencesView supporting material
Primary source
Alexander Meiners and Boris Vertman, “Spectral zeta function on discrete tori and Epstein-Riemann conjecture”, arXiv:2202.02420 (2022).
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