Some Invariants of Zd-p-Extensions.
Some linear relations between values of trigonometric functions at kπ/n
Some local-global principles in the arithmetic of algebraic groups over real function fields.
Some mean-value theorems for exponential sums
Some meromorphic functions associated to the S-unit equation
Some methods for evaluating the regulator of a real quadratic function field.
Some metric properties of subsequences
Some modular functions associated to the Lie algebra E8.
Some modular results on the Euler and Bernoulli polynomials
Some more long continued fractions, I
Some More Predictable Continued Fractions.
Some more remarks on arithmetical identities
Some new directions in -adic Hodge theory
We recall some basic constructions from -adic Hodge theory, then describe some recent results in the subject. We chiefly discuss the notion of -pairs, introduced recently by Berger, which provides a natural enlargement of the category of -adic Galois representations. (This enlargement, in a different form, figures in recent work of Colmez, Bellaïche, and Chenevier on trianguline representations.) We also discuss results of Liu that indicate that the formalism of Galois cohomology, including Tate...
Some new estimates for G(k) in Waring's problem
Some new estimates in the Dirichlet divisor problem
Some new evaluations of the Legendre symbol ((a+b√q)/p)
Some new exact van der Waerden numbers.
Some new families of Tasoevian and Hurwitzian continued fractions
Some new formulas for .
Some new infinite families of congruences modulo 3 for overpartitions into odd parts
Let denote the number of overpartitions of n in which only odd parts are used. Some congruences modulo 3 and powers of 2 for the function have been derived by Hirschhorn and Sellers, and Lovejoy and Osburn. In this paper, employing 2-dissections of certain quotients of theta functions due to Ramanujan, we prove some new infinite families of Ramanujan-type congruences for modulo 3. For example, we prove that for n, α ≥ 0, .