TITLE

Weighted Distribution of the 4-rank of Class Groups and Applications

AUTHOR(S)
Fouvry, Étienne; Klüners, Jürgen
PUB. DATE
August 2011
SOURCE
IMRN: International Mathematics Research Notices;Aug2011, Vol. 2011 Issue 16, p3618
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
We prove that the distribution of the values of the 4-rank of ideal class groups of quadratic fields is not affected when it is weighted by a divisor type function. We then give several applications concerning a new lower bound of the sums of class numbers of real quadratic fields with discriminant less than a bound tending to infinity and several questions of P. Sarnak concerning reciprocal geodesics.
ACCESSION #
64112922

 

Related Articles

  • Subgroups of Class Groups of Algebraic Quadratic Function Fields. Wang, Kunpeng; Zhang, Xianke // Chinese Annals of Mathematics;Jul2003, Vol. 24 Issue 3, p315 

    Ideal class groups H(K) of algebraic quadratic function fields K are studied. Necessary and sufficient condition is given for the class group H(K) to contain a cyclic subgroup of any order n, which holds true for both real and imaginary fields K. Then several series of function fields K,...

  • Some Results Connected with the Class Number Problem in Real Quadratic Fields. Grytczuk, Aleksander; Grytczuk, Jarosław // Acta Mathematica Sinica;Oct2005, Vol. 21 Issue 5, p1107 

    We investigate arithmetic properties of certain subsets of square-free positive integers and obtain in this way some results concerning the class number h( d) of the real quadratic field $$ \mathbb{Q}{\left( {{\sqrt d }} \right)} $$. In particular, we give a new proof of the result of Hasse,...

  • CONSTRUCTION OF CLASS FIELDS OVER IMAGINARY QUADRATIC FIELDS AND APPLICATIONS. BUMKYU CHO; JA KYUNG KOO // Quarterly Journal of Mathematics;Jun2010, Vol. 61 Issue 2, p199 

    Let K be an imaginary quadratic field, Hî”® the ring class field of an order î”® in K and K(N) be the ray class field modulo N over K for a positive integer N. In this paper we provide certain general techniques of finding Hî”® and K(N) by using the theory of Shimura's canonical...

  • A characterization of the family of external lines to a quadratic cone of PG(3, q), q. Di Gennaro, R.; Durante, N.; Olanda, D. // Journal of Geometry;2010, Vol. 96 Issue 1/2, p63 

    In this paper we characterize the family of external lines to a quadratic cone of PG(3, q), q odd, by their intersection properties with points and planes of the space.

  • EXACT COVERING SYSTEMS IN NUMBER FIELDS. Jiang, Yupeng; Deng, Yingpu // Quarterly Journal of Mathematics;Mar2014, Vol. 65 Issue 1, p211 

    It is well known that, in an exact covering system in ℤ, the biggest modulus must be repeated. Very recently, Kim gave an analogous result for certain quadratic fields, and Kim also conjectured that it must hold in any algebraic number field. In this paper, we prove Kim's conjecture. In...

  • Transitive parabolic unitals in semifield planes. Johnson, Norman // Journal of Geometry;2006, Vol. 85 Issue 1/2, p61 

    Every semifield plane with spread in PG(3, K), where K is a field admitting a quadratic extension K +, is shown to admit a transitive parabolic unital.

  • On cofinite subgroups of mapping class groups. Korkmaz, Mustafa // Turkish Journal of Mathematics;2003, Vol. 27 Issue 1, p115 

    Presents an elementary construction of a sequence G[subn] of subgroups of finite index in the mapping class group of an orientable surface of genus and in the hyperelliptic mapping class group. Definitions and preliminaries; Dimension of the second bounded cohomology group of a mapping class...

  • Realization of the mapping class group by homeomorphisms. Markovic, Vladimir // Inventiones Mathematicae;Apr2007, Vol. 168 Issue 3, p523 

    In this paper, we show that the mapping class group of a closed surface can not be geometrically realized as a group of homeomorphisms of that surface. More precisely, let $Pr:\mathcal{H}\textit{omeo}(M)\to\mathcal{M}\mathcal{C}(M)$ denote the standard projection of the group of homeomorphisms...

  • JAZ volume 100 Issue 1 Cover and Back matter.  // Journal of the Australian Mathematical Society;Feb2016, Vol. 100 Issue 1, pb1 

    The article offers information on preparation of manuscripts for the periodical and copying along with the table of contents.

Share

Read the Article

Courtesy of THE LIBRARY OF VIRGINIA

Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics