167 citations · 519 across the 84 of their papers we have counts for
6 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…
Li Coefficients for Automorphic L-Functions
Jeffrey C. Lagarias
Xian-Jin Li gave a criterion for the Riemann hypothesis in terms of the positivity of a set of coefficients lambda_n, indexed by the integers. We define similar coefficients attach…
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…
Apollonian Circle Packings: Number Theory II. Spherical and Hyperbolic Packings
Nicholas Eriksson, Jeffrey C. Lagarias
Apollonian circle packings arise by repeatedly filling the interstices between mutually tangent circles with further tangent circles. In Euclidean space it is possible for every ci…