The unramified principal series of -adic groups. I. The spherical function
The unramified principal series of -adic groups. II. The Whittaker function
The value of additive forms at prime arguments
Let be an additive form of degree with prime variables . Suppose that has real coefficients with at least one ratio algebraic and irrational. If s is large enough then takes values close to almost all members of any well-spaced sequence. This complements earlier work of Brüdern, Cook and Perelli (linear forms) and Cook and Fox (quadratic forms). The result is based on Hua’s Lemma and, for , Heath-Brown’s improvement on Hua’s Lemma.
The value of the Estermann zeta functions at s=0
The values of a quadratic form at square-free points
The View-Obstruction Problem for Spheres in ...5.
The Waring loci of ternary quartics.
The Waring-Goldbach problem for cubes
The Way to the Proof of Fermat’s Last Theorem
The weight in Serre's conjectures on modular forms.
The weight of half-integral weight modular forms with few non-vanishing coefficients mod l
The weighted linear sieve and Selberg’s -method
The Weil height in terms of an auxiliary polynomial
The Weil pairing and the Hilbert symbol.
The wildcard set's size in the density Hales-Jewett theorem.
The Witt Group of a Smooth Complex Surface.
The Witt group of quadratic characters.
The Witt ring of an elliptic curve over a local field.
The work of Gross and Zagier on Heegner points and the derivatives of -series
The work of Mazur and Wiles on cyclotomic fields