A divisibility property of binomial coefficients viewed as an elementary sieve.
A dual approach to triangle sequences: a multidimensional continued fraction algorithm.
A duality theorem in the multivariable Iwasawa theory of local fields.
A dynamical interpretation of the global canonical height on an elliptic curve.
A factorization of the Selberg zeta function attached to a rank 1 space form.
A failure of quantifier elimination.
We show that log is needed to eliminate quantifiers in the theory of the real numbers with restricted analytic functions and exponentiation.
A family of deformations of the Riemann xi-function
We introduce a family of deformations of the Riemann xi-function endowed with two continuous parameters. We show that it has rich analytic structure and that its conjectural (mild) zero-free region for some fixed parameter is a sufficient condition for the Riemann hypothesis to hold for the Riemann zeta function.
A family of elliptic ℚ-curves defined over biquadratic fields and their modularity
A family of infinite pairs of quadratic fields ℚ(√D) and ℚ(√-D) whose class numbers are both divisible by 3
A family of K3 surfaces and ... (3).
A family of meta-Fibonacci sequences defined by variable-order recursions.
A family of pseudorandom binary sequences constructed by the multiplicative inverse
A family of quartic Thue inequalities
A family of symmetric biadditive nonbilinear functions.
A fast algorithm for MacMahon's partition analysis.
A fast algorithm for polynomial factorization over
We present an algorithm that returns a proper factor of a polynomial over the -adic integers (if is reducible over ) or returns a power basis of the ring of integers of (if is irreducible over ). Our algorithm is based on the Round Four maximal order algorithm. Experimental results show that the new algorithm is considerably faster than the Round Four algorithm.
A few new facts about the EKG sequence.
A few remarks on automorphic functions.
A fibered system associated with the prime number sequence. (Sur un système fibré lié à la suite des nombres premiers.)
A Fibonacci-like sequence of composite numbers.