A new class of -Fibonacci polynomials.
A New Condition for Consecutive Primitive Roots of a Prime.
A new construction of -adic -functions attached to certain elliptic curves with complex multiplication
In this paper we apply the results of our previous article on the -adic interpolation of logarithmic derivatives of formal groups to the construction of -adic -functions attached to certain elliptic curves with complex multiplication. Our results are primarily concerned with curves with supersingular reduction.
A new construction of (t,s)-sequences and some improved bounds on their quality parameter
A new cubic character sum
A new determinant expression of the zeta function for a hypergraph.
A new domino tiling sequence.
A new equidistribution property of norms of ideals in given classes
A new exceptional polynomial for the integer transfinite diameter of
Using refinement of an algorithm given by Habsieger and Salvy to find integer polynomials with smallest sup norm on [0, 1] we extend their table of polynomials up to degree 100. For the degree 95 we find a new exceptionnal polynomial which has complex roots. Our method uses generalized Müntz-Legendre polynomials. We improve slightly the upper bound for the integer transfinite diameter of [0, 1] and give elementary proofs of lower bounds for the exponents of some critical polynomials.
A new family of Somos-like recurrences.
A new Fibonacci-like sequence of composite numbers.
A new form of the circle method, and its application to quadratic forms.
A new form of the error term in the linear sieve
A new formulation of the law of octic reciprocity for primes =+-3 (mod 8) and its consequences.
A new generating function of (-) Bernstein-type polynomials and their interpolation function.
A New Infinite Product Representation for Real Numbers.
A new interpretor for PARI/GP
When Henri Cohen and his coworkers set out to write PARI twenty years ago, GP was an afterthought. While GP has become the most commonly used interface to the PARI library by a large margin, both the gp interpretor and the GP language are primitive in design. Paradoxically, while gp allows to handle very high-level objects, GP itself is a low-level language coming straight from the seventies.We rewrote GP as a compiler/evaluator pair, implementing several high-level features (statically scoped variables,...
A new irrationality measure for ζ(3)
A new kind of Diophantine equations
A new Lehmer pair of zeros and a new lower bound for the de Bruijn-Newman constant .