Talk:Kloosterman sum

Definition

What is the inverse of x modulo m, if x=0? МетаСкептик12 (talk) 09:38, 26 May 2013 (UTC)

In the definition x and m are coprime so x is never 0. 66.130.118.9 (talk) 18:05, 13 April 2014 (UTC)

Short Kloosterman sums

It seems to me that it's given too much credit to the work of Karatsuba...--132.205.236.13 (talk) 02:12, 1 March 2014 (UTC)

The work of Karatsuba was pioneering and important, but there is a short list of people whose work must be mentioned (Bourgain, Garaev and also Korolev). Even more importantly: of the consequences mentioned, some are immediate (distribution of the inverses of n modulo p), one or two are noteworthy (e.g. the best bound for Brun-Titchmarsh), and some are only thematically linked: for instance, Heath-Brown (in the X^3+2 paper) never uses Karatsuba's work. One could say that bounds on short Kloosterman sums better than those available (in particular, better than Karatsuba's) would be useful in several ways (see the introduction to Heath-Brown's paper) but that's a very different thing.

I can edit this section if people agree. Garald (talk) 11:02, 27 September 2014 (UTC)

Yep, go ahed. About Karatsuba's work, it's true that his work is worth mentioning, however at the moment this article (dealing with Kloosterman sums in general and not only with short Kloosterman sums) gives the impression that his results were the most important on the subject, whereas other works (for example Deshouillers-Iwaniec's paper, which is only mentioned briefly) were far more influential.--70.31.201.15 (talk) 05:24, 1 October 2014 (UTC)

Agreed. We need more Kloostermania. Garald (talk) 09:23, 2 October 2014 (UTC)