Z. 9 (1921), 147-153; no 30 in [H]. 13. R. A. Rankin, George Neville Watson (obituary notice), J. London Math. Soc. Lil (1966), 551–565. lit. R.A. Rankin, The divisibility of divisor functions, Proc. Glasgow Math. Assoc. 5 (1961) ...

Author: J. P. Serre

Publisher: Springer

ISBN: 9783540372912

Category: Mathematics

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The proceedings of the conference are being published in two parts, and the present volume is mostly algebraic (congruence properties of modular forms, modular curves and their rational points, etc.), whereas the second volume will be more analytic and also include some papers on modular forms in several variables.

Cas-3 it p1(ck * h1)0 (h)v = 0 for every h1 e S (G), where ck * (meas K)-1 (characteristic function of K). ... going backwards, P2 (ck % ha) och) F(v) = 0 for all h1. which means that the G-invariant space generated by o2(h)F(v) has no ...

Author: P. Deligne

Publisher: Springer

ISBN: 9783540378556

Category: Mathematics

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Any f € 0 (M, V) can be written as a power series in u, v (this is analogous to the q-expansion in one variable. ) ... Therefore, the quotient of H*/G(M, V) U (~} by T has no singular point except possibly * , the image of oo .

Author: J.-P. Serre

Publisher: Springer

ISBN: 9783540359845

Category: Mathematics

Page: 340

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The proceedings of the conference are being published in two parts, and the present volume is mostly algebraic (congruence properties of modular forms, modular curves and their rational points, etc.), whereas the second volume will be more analytic and also include some papers on modular forms in several variables.

5 (2018), no. 1, Paper No. 3, 24 pp. 75. Kenneth A. Ribet, Galois representations attached to eigenforms with Nebentypus, Modular functions of one variable V, eds. Jean-Pierre Serre and Don Bernard Zagier, Lecture Notes in Math., vol.

Author: Jennifer S. Balakrishnan

Publisher: Springer Nature

ISBN: 9783030809140

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5 , the correspondence 6.1 reduces to the correspondence of Shimura ( 1 ) when F = Q and a is holomorphic . ... Vigneras , M.-F. ( 1977 ) Modular Functions of One Variable VI , Lecture Notes in Mathematics , No.

Author: Ilya Piatetsky-Shapiro

Publisher: American Mathematical Soc.

ISBN: 082180930X

Category: Mathematics

Page: 824

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This selection of papers of I. Piatetski-Shapiro represents almost 50 years of his mathematical activity. Included are many of his major papers in harmonic analysis, number theory, discrete groups, bounded homogeneous domains, algebraic geometry, automorphic forms, and automorphic $L$-functions. The papers in the volume are intended as a representative and accurate reflection of both the breadth and depth of Piatetski-Shapiro's work in mathematics. Some of his early works, such as those on the prime number theorem and on sets of uniqueness for trigonometric series, appear for the first time in English. Also included are several commentaries by his close colleagues. This volume offers an elegant representation of the contributions made by this renowned mathematician.

R. A. Rankin, The divisibility of divisor functions, Glasgow Math. J. 5 (1961), 35–40. R. A. Rankin, Ramanujan's unpublished work on congruences, Modular Functions of One Variable V, Lecture Notes in Math., No.

Author: Dominique Foata

Publisher: Springer Science & Business Media

ISBN: 9783642565137

Category: Mathematics

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This book contains seventeen contributions made to George Andrews on the occasion of his sixtieth birthday, ranging from classical number theory (the theory of partitions) to classical and algebraic combinatorics. Most of the papers were read at the 42nd session of the Sminaire Lotharingien de Combinatoire that took place at Maratea, Basilicata, in August 1998. This volume contains a long memoir on Ramanujan's Unpublished Manuscript and the Tau functions studied with a contemporary eye, together with several papers dealing with the theory of partitions. There is also a description of a maple package to deal with general q-calculus. More subjects on algebraic combinatorics are developed, especially the theory of Kostka polynomials, the ice square model, the combinatorial theory of classical numbers, a new approach to determinant calculus.

R.A. Rankin, The divisibility of divisor functions, Glasgow Math. J. 5 (1961), 35–40. R.A. Rankin, Ramanujan's unpublished work on congruences, in Modular Functions of One Variable V, Lecture Notes in Math. No.

Author: George E. Andrews

Publisher: Springer Science & Business Media

ISBN: 9781461438106

Category: Mathematics

Page: 436

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In the spring of 1976, George Andrews of Pennsylvania State University visited the library at Trinity College, Cambridge to examine the papers of the late G.N. Watson. Among these papers, Andrews discovered a sheaf of 138 pages in the handwriting of Srinivasa Ramanujan. This manuscript was soon designated, "Ramanujan's lost notebook." Its discovery has frequently been deemed the mathematical equivalent of finding Beethoven's tenth symphony. This volume is the third of five volumes that the authors plan to write on Ramanujan’s lost notebook and other manuscripts and fragments found in The Lost Notebook and Other Unpublished Papers, published by Narosa in 1988. The ordinary partition function p(n) is the focus of this third volume. In particular, ranks, cranks, and congruences for p(n) are in the spotlight. Other topics include the Ramanujan tau-function, the Rogers–Ramanujan functions, highly composite numbers, and sums of powers of theta functions. Review from the second volume: "Fans of Ramanujan's mathematics are sure to be delighted by this book. While some of the content is taken directly from published papers, most chapters contain new material and some previously published proofs have been improved. Many entries are just begging for further study and will undoubtedly be inspiring research for decades to come. The next installment in this series is eagerly awaited." - MathSciNet Review from the first volume: "Andrews a nd Berndt are to be congratulated on the job they are doing. This is the first step...on the way to an understanding of the work of the genius Ramanujan. It should act as an inspiration to future generations of mathematicians to tackle a job that will never be complete." - Gazette of the Australian Mathematical Society

J. 50 (1983), no. 2, 487–504, DOI 10.1215/S0012-7094-83-05021-4. MR705036 [9] V. Kumar Murty, Arithmetic twists and abelian extensions, this volume. [10] K. A. Ribet, Modular functions of one variable V (Bonn, 1976), pp.

Author: Joan-Carles Lario

Publisher: American Mathematical Soc.

ISBN: 9781470419912

Category: Forms, Modular

Page: 232

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This volume contains the proceedings of the Barcelona-Boston-Tokyo Number Theory Seminar, which was held in memory of Fumiyuki Momose, a distinguished number theorist from Chuo University in Tokyo. Momose, who was a student of Yasutaka Ihara, made important contributions to the theory of Galois representations attached to modular forms, rational points on elliptic and modular curves, modularity of some families of Abelian varieties, and applications of arithmetic geometry to cryptography. Papers contained in this volume cover these general themes in addition to discussing Momose's contributions as well as recent work and new results.

BIBLIOGRAPHIE [ 1 ] A. ATKIN , J. LEHNER.- Hecke operators on r ( m ) , Math . Ann . , 185 , ( 1970 ) , p . 134-160 . [ 2 ] B.J. BIRCH , W. KUYK ( ed . ) .- Numerical tables on elliptic curves , in Modular Functions of One Variable IV ...

Author: Jean-Pierre Serre

Publisher:

ISBN: UOM:39015049302527

Category: Algebraic number theory

Page: 294

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S. Ramanujan, Highly composite numbers, Annotated by J.-L. Nicolas and G. Robin, The Ramanujan J. 1 (1997), ... R. A. Rankin, Ramanu3an's unpublished work on congruences, Modular Functions of One Variable, V, Lecture Notes in Math., No.

Author: Srinivasa Ramanujan Aiyangar

Publisher: American Mathematical Soc.

ISBN: 9780821820766

Category: Mathematics

Page: 426

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The influence of Ramanujan on number theory is without parallel in mathematics. His papers, problems and letters have spawned a remarkable number of later results by many different mathematicians. Here, his 37 published papers, most of his first two and last letters to Hardy, the famous 58 problems submitted to the Journal of the Indian Mathematical Society, and the commentary of the original editors (Hardy, Seshu Aiyar and Wilson) are reprinted again, after having been unavailable for some time. In this, the third printing of Ramanujan's collected papers, Bruce Berndt provides an annotated guide to Ramanujan's work and to the mathematics it inspired over the last three-quarters of a century. The historical development of ideas is traced in the commentary and by citations to the copious references. The editor has done the mathematical world a tremendous service that few others would be qualified to do.