2 citations · 2 across the 9 of their papers we have counts for
9 papers · 1 filter
The Riemann hypothesis for certain integrals of Eisenstein series
Jeffrey C. Lagarias, Masatoshi Suzuki
This paper studies the non-holomorphic Eisenstein series E(z,s) for the modular surface, and shows that integration with respect to certain non-negative measures gives meromorphic…
Wild and Wooley Numbers
Jeffrey C. Lagarias
This paper studies the multiplicative semigroup generated by all rationals of the form (3n+2)/(2n+1) for nonnegative integers n, together with 1/2. The subsemigroup of integers in…
The 3x+1 Semigroup
David Applegate, Jeffrey C. Lagarias
The 3x+1 semigroup is the multiplicative semigroup generated by the rational numbers of form (2k+1)/(3k+2) for non-negative k, together with 2. This semigroup encodes backward iter…
A Note on Absolute Derivations and Zeta Functions
Jeffrey C. Lagarias
This comment answers a question raised by Kurokawa, Ochiai and Wakayama whether a certain operator constructed using a notion of quantum non-commutativity of primes has eigenvalues…
The EKG Sequence
J. C. Lagarias, E. M. Rains, N. J. A. Sloane
The EKG or electrocardiogram sequence is defined by a(1) = 1, a(2) = 2 and, for n >= 3, a(n) is the smallest natural number not already in the sequence with the property that gcd {…
Lower bounds for the total stopping time of 3X+1 iterates
David Applegate, Jeffrey C. Lagarias
The 3X+1 function T(n) is (3n+1)/2 if n is odd and n/2 if n is even. The total stopping time σ_\infty (n) for a positive integer n is the number of iterations of the 3x+1 function…