# Some Results Connected with the Class Number Problem in Real Quadratic Fields

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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...

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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.

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In mathematics, numbers that satisfy a polynomial equation with rational coefficients: for example, âˆš2 solves x2 - 2 = 0. Real numbers that are not algebraic are called

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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...

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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,...

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Given a function f : E â†’ R with E âŠ‚ ℝ:n, we explain how to decide whether f extends to a âŠ‚m function F on â„n. If E is finite, then one can efficiently compute an F as above, whose Cm norm has the least possible order of magnitude (joint work with B. Klartag).

- Generalized Formal Degree. Qiu, Yannan // IMRN: International Mathematics Research Notices;Jan2012, Vol. 2012 Issue 2, p239
Let G be a reductive group over a local field of characteristic zero or a finite central cover of such a group. We present a conjecture that enables one to define formal degree for all unitary representations of G. The conjecture is proved for GLn and over real and p-adic fields, together with a...

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The distribution of special algebraic numbers is studied, and an optimal regular system is constructed. Bibliography: 11 titles.

- 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.