The Bump-Ng theorem (and also the title of the paper in which it was proved) states that the zeros of the Mellin transform of Hermite functions have real part equal to 1/2.
Bump-Ng Theorem
See also
Mellin TransformExplore with Wolfram|Alpha
References
Bump, D. and Ng, K.-S. "The Zeros of the Mellin Transform of Hermite Functions Have Real Part One-Half." 1986.Derbyshire, J. Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics. New York: Penguin, pp. 352 and 391, 2004.Referenced on Wolfram|Alpha
Bump-Ng TheoremCite this as:
Weisstein, Eric W. "Bump-Ng Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Bump-NgTheorem.html