De Bruijn–Newman constant

The real constant Λ is the threshold parameter for a deformation of the Riemann xi function: its zeros are all real exactly when the parameter is at least Λ.

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De Bruijn–Newman function: The family of entire functions whose zeros determine the De Bruijn–Newman constant. Its parameter-dependent zeros supply the threshold that defines Λ.
Riemann hypothesis: The conjecture that every nontrivial zero of the Riemann zeta function has real part one-half. The hypothesis is equivalent to Λ being nonpositive.
George Pólya: A Hungarian mathematician known for work in analysis, probability, and problem-solving. His investigations into Fourier transforms and real zeros helped shape the questions behind the constant.
Rodgers–Tao theorem: A theorem proving that the De Bruijn–Newman constant is nonnegative. It established Newman’s conjecture and ruled out a negative threshold.
Riemann xi function: An entire function whose zeros encode the nontrivial zeros of the Riemann zeta function. The deformation underlying Λ begins with this function.
Newman’s conjecture: The conjecture that the De Bruijn–Newman constant is nonnegative. It asserts that the threshold cannot lie below zero.
Nikolai Nikolaevich Meiman: A Soviet mathematician who studied entire functions and the zeros of transforms related to the zeta function. His work contributed to the development of the deformation framework.
Terry Tao: An Australian mathematician whose work spans harmonic analysis, partial differential equations, and number theory. He co-authored the proof that Λ is nonnegative.
Heat equation: A partial differential equation describing diffusion of a quantity through space over time. The function family can be expressed through backward heat flow, which drives zero motion.
Riemann zeta function: A complex function defined initially by a series over positive integers and continued meromorphically. Its nontrivial zeros are encoded by the xi function used to define Λ.