By Fred Diamond,Jerry Shurman
This booklet introduces the speculation of modular varieties, from which all rational elliptic curves come up, with an eye fixed towards the Modularity Theorem. dialogue covers elliptic curves as advanced tori and as algebraic curves; modular curves as Riemann surfaces and as algebraic curves; Hecke operators and Atkin-Lehner conception; Hecke eigenforms and their mathematics homes; the Jacobians of modular curves and the Abelian forms linked to Hecke eigenforms. because it provides those rules, the publication states the Modularity Theorem in quite a few types, bearing on them to one another and concerning their purposes to quantity idea. The authors think no historical past in algebraic quantity thought and algebraic geometry. routines are included.
Read Online or Download A First Course in Modular Forms (Graduate Texts in Mathematics) PDF
Similar number theory books
Quantity thought was famously categorized the queen of arithmetic through Gauss. The multiplicative constitution of the integers specifically offers with many desirable difficulties a few of that are effortless to appreciate yet very tough to solve. long ago, quite a few very diversified options has been utilized to additional its figuring out.
Within the spring of 1976, George Andrews of Pennsylvania country college visited the library at Trinity university, Cambridge, to ascertain the papers of the overdue G. N. Watson. between those papers, Andrews came across a sheaf of 138 pages within the handwriting of Srinivasa Ramanujan. This manuscript was once quickly precise "Ramanujan's misplaced laptop.
This publication delineates a number of the varieties of factorization difficulties for matrix and operator features. the issues originate from, or are prompted through, the idea of non-selfadjoint operators, the idea of matrix polynomials, mathematical structures and keep an eye on conception, the idea of Riccati equations, inversion of convolution operators, and the idea of activity scheduling in operations learn.
A hugely profitable presentation of the basic techniques of quantity thought and desktop programming Bridging an latest hole among arithmetic and programming, basic quantity thought with Programming presents a special creation to trouble-free quantity idea with basic assurance of desktop programming.
Additional resources for A First Course in Modular Forms (Graduate Texts in Mathematics)