Fourier coefficients of cusp forms with half-integral weight
| Author | : Xiangdong Wang |
| Publisher | : |
| Total Pages | : 18 |
| Release | : 1993 |
| Genre | : |
| ISBN | : |
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Fourier Coefficients of Modular Forms of Half-integral Weight
| Author | : W. Kohnen |
| Publisher | : |
| Total Pages | : 39 |
| Release | : 1984 |
| Genre | : |
| ISBN | : |
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Modular Forms with Integral and Half-Integral Weights
| Author | : Xueli Wang |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 436 |
| Release | : 2013-02-20 |
| Genre | : Mathematics |
| ISBN | : 3642293026 |
Download Modular Forms with Integral and Half-Integral Weights Book in PDF, ePub and Kindle
"Modular Forms with Integral and Half-Integral Weights" focuses on the fundamental theory of modular forms of one variable with integral and half-integral weights. The main theme of the book is the theory of Eisenstein series. It is a fundamental problem to construct a basis of the orthogonal complement of the space of cusp forms; as is well known, this space is spanned by Eisenstein series for any weight greater than or equal to 2. The book proves that the conclusion holds true for weight 3/2 by explicitly constructing a basis of the orthogonal complement of the space of cusp forms. The problem for weight 1/2, which was solved by Serre and Stark, will also be discussed in this book. The book provides readers not only basic knowledge on this topic but also a general survey of modern investigation methods of modular forms with integral and half-integral weights. It will be of significant interest to researchers and practitioners in modular forms of mathematics. Dr. Xueli Wang is a Professor at South China Normal University, China. Dingyi Pei is a Professor at Guangzhou University, China.
Distribution of Integral Fourier Coefficients of a Modular Form of Half Integral Weight Modulo Primes
| Author | : |
| Publisher | : |
| Total Pages | : |
| Release | : 2007 |
| Genre | : |
| ISBN | : |
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Recently, Bruinier and Ono classified cusp forms $f(z) := \sum_{n=0}^{\infty} a_f(n)q ^n \in S_{\lambda+1/2}(\Gamma_0(N), \chi)\cap \mathbb{Z}[[q]]$ that does not satisfy a certain distribution property for modulo odd primes $p$. In this paper, using Rankin-Cohen Bracket, we extend this result to modular forms of half integral weight for primes $p \geq 5$. As applications of our main theorem we derive distribution properties, for modulo primes $p\geq5$, of traces of singular moduli and Hurwitz class number. We also study an analogue of Newman's conjecture for overpartitions.
Modular Functions of One Variable, I-IV
| Author | : Willem Kuyk |
| Publisher | : |
| Total Pages | : |
| Release | : 1973 |
| Genre | : Modular functions |
| ISBN | : |
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A First Course in Modular Forms
| Author | : Fred Diamond |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 462 |
| Release | : 2006-03-30 |
| Genre | : Mathematics |
| ISBN | : 0387272267 |
Download A First Course in Modular Forms Book in PDF, ePub and Kindle
This book introduces the theory of modular forms, from which all rational elliptic curves arise, with an eye toward the Modularity Theorem. Discussion covers elliptic curves as complex tori and as algebraic curves; modular curves as Riemann surfaces and as algebraic curves; Hecke operators and Atkin-Lehner theory; Hecke eigenforms and their arithmetic properties; the Jacobians of modular curves and the Abelian varieties associated to Hecke eigenforms. As it presents these ideas, the book states the Modularity Theorem in various forms, relating them to each other and touching on their applications to number theory. The authors assume no background in algebraic number theory and algebraic geometry. Exercises are included.
Relations Between Fourier Coefficients of Nonholomorphic Hilbert Modular Forms of Half-integral Weight and Special Values of Dirichlet Series
| Author | : Kamal Khuri-Makdisi |
| Publisher | : |
| Total Pages | : 156 |
| Release | : 1993 |
| Genre | : |
| ISBN | : |
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Toric Periods and $p$-adic Families of Modular Forms of Half-Integral Weight
| Author | : V. Vatsal |
| Publisher | : American Mathematical Society |
| Total Pages | : 108 |
| Release | : 2023-09-27 |
| Genre | : Mathematics |
| ISBN | : 1470465507 |
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The 1-2-3 of Modular Forms
| Author | : Jan Hendrik Bruinier |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 273 |
| Release | : 2008-02-10 |
| Genre | : Mathematics |
| ISBN | : 3540741194 |
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This book grew out of three series of lectures given at the summer school on "Modular Forms and their Applications" at the Sophus Lie Conference Center in Nordfjordeid in June 2004. The first series treats the classical one-variable theory of elliptic modular forms. The second series presents the theory of Hilbert modular forms in two variables and Hilbert modular surfaces. The third series gives an introduction to Siegel modular forms and discusses a conjecture by Harder. It also contains Harder's original manuscript with the conjecture. Each part treats a number of beautiful applications.
The Theory of Jacobi Forms
| Author | : Martin Eichler |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 156 |
| Release | : 2013-12-14 |
| Genre | : Mathematics |
| ISBN | : 1468491628 |
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The functions studied in this monogra9h are a cross between elliptic functions and modular forms in one variable. Specifically, we define a Jacobi form on SL (~) to be a holomorphic function 2 (JC = upper half-plane) satisfying the t\-10 transformation eouations 2Tiimcz· k CT +d a-r +b z) (1) ((cT+d) e cp(T, z) cp CT +d ' CT +d (2) rjl(T, z+h+]l) and having a Four·ier expansion of the form 00 e2Tii(nT +rz) (3) cp(T, z) 2: c(n, r) 2:: rE~ n=O 2 r ~ 4nm Here k and m are natural numbers, called the weight and index of rp, respectively. Note that th e function cp (T, 0) is an ordinary modular formofweight k, whileforfixed T thefunction z-+rjl( -r, z) isa function of the type normally used to embed the elliptic curve ~/~T + ~ into a projective space. If m= 0, then cp is independent of z and the definition reduces to the usual notion of modular forms in one variable. We give three other examples of situations where functions satisfying (1)-(3) arise classically: 1. Theta series. Let Q: ~-+ ~ be a positive definite integer valued quadratic form and B the associated bilinear form.
