Journal of the Ramanujan Mathematical Society
https://i-scholar.in/index.php/rms
After RMS was founded in 1985, the starting of its journal - Journal of the Ramanujan Mathematical Society (JRMS) - followed as a sequitur in 1986. As one who mooted the idea of starting the journal, the mantle of Editor-in-Chief fell naturally upon Professor K.S. Padmanabhan. He put it on a solid foundation during the period 1986-1991 of his chief editorship so that it could shape into a truly international journal. Professor V. Kannan succeeded him in 1992 and continued in this capacity till 1996. Professor Kumar Murty took over the Chief Editorship in 1997. Embedded as he is in the pride of Indian nationalism, Professor Kumar Murty has chosen a team of relatively young but accomplished mathematicians, all Indian, as his associate editors for the JRMS . Under his stewardship, JRMS has witnessed a meteoric rise that could be seen from the fact that the American Mathematical Society (AMS) came forward to undertake the distribution of JRMS outside India. To start with, it had ordered for 25 copies; this was later raised to 40 and then to 50. Apart from this, there are some 105 Indian subscribers, too. The journal is also being mailed free to all the members of the Society who opted for it in the membership form. To start with, JRMS had two issues per year. Now it has four issues per year and it is proposed to increase the number to six possibly from next year. True to the wishes of the founders of RMS, the journal maintains both quality and regularity, the quality is being taken care of by the Editor-in-Chief and his associates and regularity, by the untiring efforts of the Managing Editor Professor Sampathkumar.en-USesampathkumar@gmail.com (E. Sampath Kumar)esampathkumar@gmail.com (E. Sampath Kumar)Sun, 01 Dec 2019 00:00:00 +0000OJS 2.4.2.0http://blogs.law.harvard.edu/tech/rss60On Klingen Eisenstein Series with Level in Degree Two
https://i-scholar.in/index.php/rms/article/view/191316
We give a representation theoretic approach to the Klingen lift in degree 2, generalizing the classical construction of Klingen Eisenstein series to arbitrary levels for both paramodular and Siegel congruence subgroups.Ralf Schmidt, Alok Shuklahttps://i-scholar.in/index.php/rms/article/view/191316Sun, 01 Dec 2019 00:00:00 +0000A Short Note on the Divisibility of Class Numbers of Real Quadratic Fields
https://i-scholar.in/index.php/rms/article/view/191317
For any integer l ≥ 1, let p1, p2, . . . , p<sub>l+2</sub> be distinct prime numbers ≥ 5. For all real numbers X > 1, we let N3,l (X) denote the number of real quadratic fields K whose absolute discriminant dK ≤ X and dK is divisible by (p1 . . . p<sub>l+2</sub>) together with the class number hK of K divisible by 2<sup>l</sup> · 3. Then, in this short note, by following the method in [3], we prove that N3,l (X) ≫ X <sup>7/8</sup> for all large enough X’s.Jaitra Chattopadhyayhttps://i-scholar.in/index.php/rms/article/view/191317Sun, 01 Dec 2019 00:00:00 +0000A Note on Depth Preservation
https://i-scholar.in/index.php/rms/article/view/191318
We show that for a wildly ramified torus, depth is not preserved in general under local Langlands correspondence for tori.Manish Mishra, Basudev Pattanayakhttps://i-scholar.in/index.php/rms/article/view/191318Sun, 01 Dec 2019 00:00:00 +0000Interpreting Some Fifth and Sixth Order Mock Theta Functions by Attaching Weights
https://i-scholar.in/index.php/rms/article/view/191319
A constructive approach is applied to obtain the interpretations of two mock theta functions of order five and four of order six using two-line arrays for (n + t)–color partitions. Interpretations of four mock theta functions are obtained by attaching weights to the partitions generated by their unsigned versions. Further, mappings are established to obtain the interpretations of the same mock theta functions in terms of F–partitions.S. Sharma, M. Ranahttps://i-scholar.in/index.php/rms/article/view/191319Sun, 01 Dec 2019 00:00:00 +0000A Note on the Arithmetic Chowla-Milnor Space
https://i-scholar.in/index.php/rms/article/view/191320
Milnor, motivated by a work of P. Chowla and S. Chowla, formulated a conjecture about linear independence of some special Hurwitz zeta values over the field of rational numbers. In [7,8], Gun, <em>et al</em>. derived non-trivial lower bounds of the dimension of the space generated by these Hurwitz zeta values over certain family of number fields. This they did by working with a natural subspace. In this note, we study the dimensions of these canonical subspaces over any arbitrary number field.Abhishek T. Bharadwajhttps://i-scholar.in/index.php/rms/article/view/191320Sun, 01 Dec 2019 00:00:00 +0000New Infinite Families of Congruences Modulo 3, 5 and 7 For Overpartition Function
https://i-scholar.in/index.php/rms/article/view/191321
Let ¯p(n) denote the number of overpartitions of a non-negative integer n. In this paper, we prove two new infinite families of congruences modulo 3 for ¯p(n) by using Ramanujan’s theta-function identities. Particularly, we prove that, for any integer α ≥ 0, ¯p(9<sup>α+1</sup>(24n + 23)) ≡ 0 (mod 3) and ¯p(9<sup>α+1</sup>(24n + 22) + 1) ≡ 0 (mod 3). Furthermore, we prove some new congruences modulo 5 and 7 for ¯p(n). For example, we prove that ¯p(5n+k+3) ≡ 0 (mod 5), where k = 3n<sup>2</sup> ± n.Jubaraj Chetry, Nipen Saikiahttps://i-scholar.in/index.php/rms/article/view/191321Sun, 01 Dec 2019 00:00:00 +0000Existence of Euclidean Ideal Classes Beyond Certain Rank
https://i-scholar.in/index.php/rms/article/view/191322
In his seminal paper on Euclidean ideal classes, Lenstra showed that under generalised Riemann hypothesis, a number field K has a Euclidean ideal class if and only if the class group is cyclic. In [3], the authors show that under certain conditions on the Hilbert class field of the number field K, for unit rank greater than or equal to 3, K has a Euclidean ideal class if and only if the class group is cyclic. The main objective of this article is to give a short alternate proof of the fact that, under similar conditions, there exists an integer r ≥ 1 such that all fields with unit rank greater than or equal to r have a Euclidean ideal class if and only if the class group is cyclic. The main novelty of this proof is that we use Brun’s sieve as opposed to the linear sieve as seen traditionally in the context of this problem.Jyothsnaa Sivaramanhttps://i-scholar.in/index.php/rms/article/view/191322Sun, 01 Dec 2019 00:00:00 +0000Some Explicit Computations in Arakelov Geometry of Abelian Varieties
https://i-scholar.in/index.php/rms/article/view/191323
Given a polarized complex abelian variety (A, L), a Gromov lemma makes a comparison between the sup and L<sup>2</sup> norms of a global section of L. We give here an explicit bound which depends on the dimension, degree and injectivity diameter of (A, L). It rests on a more general estimate for the jet of a global section of L. As an application we deduce some estimates of the maximal slope of the tangent and cotangent spaces of a polarized abelian variety defined over a number field. These results are effective versions of previous works by Masser and W¨ustholz on one hand and Bost on the other. They also improve some similar statements established by Graftieaux in 2000.Eric Gaudronhttps://i-scholar.in/index.php/rms/article/view/191323Sun, 01 Dec 2019 00:00:00 +0000Semi-stability of the Pullback of T<sub>𝕡</sub>2 on an Elliptic Curve
https://i-scholar.in/index.php/rms/article/view/191324
We study semi-stability of the pullback of the tangent bundle T<sub>𝕡</sub>2 on an elliptic curve under the morphism given by a line bundle of degree less or equal to 4.Amit Kumar Singhhttps://i-scholar.in/index.php/rms/article/view/191324Sun, 01 Dec 2019 00:00:00 +0000A Note on Generalizations of Stieltjes Constants
https://i-scholar.in/index.php/rms/article/view/191325
In this article we consider a generalization of Stieltjes constants and study its relation with special values of certain Dirichlet series. Further we show a connection of these constants with a generalization of Digamma function. Some of the results obtained are a natural generalization of the identities of Gauss, Lehmer, Dilcher and many other authors.Tapas Chatterjee, Suraj Singh Khuranahttps://i-scholar.in/index.php/rms/article/view/191325Sun, 01 Dec 2019 00:00:00 +0000