Distribution Of Class Numbers Research Articles

KONSERVASI HUTAN PADA JURNAL BIOLOGI INDONESIA PERIODE 2010-2020: SEBUAH STUDI BIBLIOMETRIK

A bibliometric analysis was carried out on the Indonesian Biology Journal for the period 2010 – 2020, with the aim of knowing 1) the distribution of keywords to see the description of the research published in the Indonesian Biology Journal 2010-2020; 2) article classification; 3) distribution of articles by year; 4) distribution of articles by issue number; 5) authorship pattern; 6) the most prolific writer; 7) affiliations of authors who contribute to the Indonesian Biology Journal; 8) the type of document used as a reference in the Indonesian Biology Journal 2010-2020. The bibliometric method was used, and the data was taken from the Indonesian Biology Journal from 2010 to 2020, which was downloaded via the address https://e-journal.biologi.lipi.go.id/index.php/jurnal_biologi_indonesia. Furthermore, the analysis of the distribution of articles based on keywords, distribution of class numbers, distribution of articles by year, distribution of articles by number of publications, pattern of authorship, most productive authors, pattern of authorship affiliation was carried out. Based on the results and discussion, it can be concluded that during 2010-2020, 315 article titles have been published and there are 1,343 keywords. Of the 50 most keywords, the keyword Biodiversity often appears 21 times (1.56%) then Genetic variation and Wildlife conservation each 20 times (1.48%), then Animal population 18 times (1.34 %), followed by Plant conservation 17 times (1.19%) and Animal conservation 16 times (1.19%). Next is Feeds and Plant growth substances each with 15 (1.11%), then In vitro culture and Plant diversity each with 14 (1.04%). Next, Vegetation is 13 (0.90%), followed by Habitat conservation and Plant species, each with 11 (0.82%). On the order of 50 keywords Drought resistance, with a total of 4 (0.29%). The highest class is class 635 with a frequency of 35 (11.11%). Articles written by a single author (71 titles; 22.54%) and articles written by collaboration (244 titles; 77.46%). the least number of articles published is in 2020, which is 1 article title (3,17). For issue number 1 starting from volume 6 to volume 16, 164 article titles have been published (52.06%). As for number 2 with the same volume, there were 151 article titles (47.94%). The most prolific writer is Hellen Kurniati with 13 writings, followed by Wartika Rosa Farida with 12 writings and then Witjaksono with 11 writings. Then Andri Permata Sari, Niken Tunjung Murti Pratiwi, NLP. Indi Dharmayanti, Tri Muji Ermayanti with 10 each, followed by Didik Widyatmoko and Risa Indriani with 9 each, Atit Kanti and Yopi with 7 each and Dwi Astuti, Eko Sulistyadi, Ibnu Maryanto, Inna Puspa Ayu each. 6 posts. LIPI is the first institution that contributes the most articles, with a frequency of 260 times. It is known that 7,354 document titles are used as references and the journal is in the first order of cited documents, with 4,591 titles (62.42%).

Distribution of Class Numbers in Continued Fraction Families of Real Quadratic Fields

AbstractWe construct a random model to study the distribution of class numbers in special families of real quadratic fields ${\open Q}(\sqrt d )$ arising from continued fractions. These families are obtained by considering continued fraction expansions of the form $\sqrt {D(n)} = [f(n),\overline {u_1,u_2, \ldots ,u_{s-1} ,2f(n)]} $ with fixed coefficients u1, …, us−1 and generalize well-known families such as Chowla's 4n2 + 1, for which analogous results were recently proved by Dahl and Lamzouri [‘The distribution of class numbers in a special family of real quadratic fields’, Trans. Amer. Math. Soc. (2018), 6331–6356].

The distribution of class numbers in a special family of real quadratic fields

We investigate the distribution of class numbers in the family of real quadratic fields Q ( d ) \mathbb {Q}(\sqrt {d}) corresponding to fundamental discriminants of the form d = 4 m 2 + 1 d=4m^2+1 , which we refer to as Chowla’s family. Our results show a strong similarity between the distribution of class numbers in this family and that of class numbers of imaginary quadratic fields. As an application of our results, we prove that the average order of the number of quadratic fields in Chowla’s family with class number h h is ( log ⁡ h ) / 2 G (\log h)/2G , where G G is Catalan’s constant. With minor modifications, one can obtain similar results for Yokoi’s family of real quadratic fields Q ( d ) \mathbb {Q}(\sqrt {d}) , which correspond to fundamental discriminants of the form d = m 2 + 4 d=m^2+4 .

On a question of Hayes concerning integrality of Brumer elements

To every abelian Galois extension K / k of number fields with group G, one can associate a so-called Brumer element \(\theta _{K/k,S}\) of the rational group ring \(\mathbb Q[G]\) (depending on another technical parameter S). In a certain sense this element can be thought of as an equivariant version of the class number \(h_K\). There is a slight problem since this element is only “almost” integral (that is, it may have non-integral coefficients). The potential denominators always divide \(w_K\), the number of roots of unity in K. Hayes (Contemp Math 358:193–205, 2004) raised the question whether the Brumer element will be p-integral under certain suitable hypotheses, one of which implies that p divides \(h_K\); of course only situations with \(p|w_K\) are of interest. This paper answers this question in the negative. We start with an “almost counterexample” over \(\mathbb Q\) (for \(k=\mathbb {Q}\) there are no true counterexamples) and manufacture true counterexamples in which k is a suitable real quadratic field. Using deep recent results on the distribution of class numbers (Bhargava et al.) one can show that the method in fact yields infinitely many counterexamples.

On Cyclic Cubic Fields

A table of class numbers and units in cyclic cubic fields with conductor $< 4000$ has been given by Marie-Nicole Gras [6]. The authors have constructed an extended table for conductor $< 16000$. The article comprises lists of fields with totally positive fundamental units and fields in which the class group has a Sylow p-subgroup which is not elementary abelian. We also give statistics about the distribution of class numbers.

On Totally Real Cubic Fields

The authors have constructed a table of the 26440 nonconjugate totally real cubic number fields of discriminant $D < 500000$ thereby extending the existing table of fields with $D < 100000$ by I. O. Angell [1]. Serious defects in Angell’s table are pointed out. For each field, running number, discriminant, coefficients of a generating polynomial, integral basis, class number, and a fundamental pair of units are listed. The article contains statistics about the following subjects: distribution of class numbers; fields in which every norm-positive unit is totally positive; nonconjugate fields with the same discriminant; fields with noncyclic class group. The fields are tabulated by means of a method due to Davenport and Heilbronn [7], [8] which leads to a unique normalized generating polynomial. The given units are chosen so that the fundamental parallelogram of the unit lattice determined by the corresponding vectors in the logarithmic space is reduced.

On cyclic cubic fields

A table of class numbers and units in cyclic cubic fields with conductor &gt; 4000 &gt; 4000 has been given by Marie-Nicole Gras [6]. The authors have constructed an extended table for conductor &gt; 16000 &gt; 16000 . The article comprises lists of fields with totally positive fundamental units and fields in which the class group has a Sylow p-subgroup which is not elementary abelian. We also give statistics about the distribution of class numbers.

On totally real cubic fields

The authors have constructed a table of the 26440 nonconjugate totally real cubic number fields of discriminant D &gt; 500000 D &gt; 500000 thereby extending the existing table of fields with D &gt; 100000 D &gt; 100000 by I. O. Angell [1]. Serious defects in Angell’s table are pointed out. For each field, running number, discriminant, coefficients of a generating polynomial, integral basis, class number, and a fundamental pair of units are listed. The article contains statistics about the following subjects: distribution of class numbers; fields in which every norm-positive unit is totally positive; nonconjugate fields with the same discriminant; fields with noncyclic class group. The fields are tabulated by means of a method due to Davenport and Heilbronn [7], [8] which leads to a unique normalized generating polynomial. The given units are chosen so that the fundamental parallelogram of the unit lattice determined by the corresponding vectors in the logarithmic space is reduced.

Computation of the ideal class group of certain complex quartic fields. II

For quartic fields K = F 3 ( π ) K = {F_3}(\sqrt \pi ) , where F 3 = Q ( ρ ) {F_3} = Q(\rho ) and π ≡ 1 mod 4 \pi \equiv 1 \bmod 4 is a prime of F 3 {F_3} , the ideal class group is calculated by the same method used previously for quadratic extensions of F 1 = Q ( i ) {F_1} = Q(i) , but using Hurwitz’ complex continued fraction over Q ( ρ ) Q(\rho ) . The class number was found for 10000 such fields, and the previous computation over F 1 {F_1} was extended to 10000 cases. The distribution of class numbers is the same for 10000 fields of each type: real quadratic, quadratic over F 1 {F_1} , quadratic over F 3 {F_3} . Many fields were found with non-cyclic class group, including the first known real quadratics with groups 5 × 5 5 \times 5 and 7 × 7 7 \times 7 . Further properties of the continued fractions are also discussed.