On a Theorem of Bombieri, Friedlander, and Iwaniec

The Friedlander–iwaniec Character Sum

As we observed in [3], one can also interpret the sums S(α;β) as special cases of the correlation sums arising in our work on algebraic twists of modular forms, and we also noted that our more general results and techniques had, as special case, this theorem of Birch and Bombieri. Very recently, Y. Zhang [12, Lemma 12] made a crucial use of this estimate in his work on bounded gaps between prim...

On a Theorem of Bombieri-vinogradov Type

for any e > 0 and A > 0, the implied constant in the symbol <g depending at most on E and A (see [1] and [14]). The original proofs of Bombieri and Vinogradov were greatly simplified by P. X. Gallagher [4]. An elegant proof has been given recently by R. C. Vaughan [13]. For other references see H. L. Montgomery [10] and H. -E. Richert [12]. Estimates of type (1) are required in various applicat...

Note on a Theorem of Bousfield and Friedlander

We examine the proof of a classical localization theorem of Bousfield and Friedlander and we remove the assumption that the underlying model category be right proper. The key to the argument is a lemma about factoring in morphisms in the arrow category of a model category.

The Bombieri-vinogradov Theorem

A Bombieri-vinogradov Theorem for All Number Fields

Abstract. The classical theorem of Bombieri and Vinogradov is generalized to a non-abelian, non-Galois setting. This leads to a prime number theorem of “mixed-type” for arithmetic progressions “twisted” by splitting conditions in number fields. One can view this as an extension of earlier work of M. R. Murty and V. K. Murty on a variant of the Bombieri-Vinogradov theorem. We develop this theory...