The theory of elliptic curves and modular forms provides a fruitful meeting ground for such diverse areas as number theory, complex analysis, algebraic geometry, and representation theory. This book starts out with a problem from elementary number theory and proceeds to lead its reader into the mod...
The theory of elliptic curves and modular forms provides a fruitful meeting ground for such diverse areas as number theory, complex analysis, algebraic geometry, and representation theory. This book starts out with a problem from elementary number theory and proceeds to lead its reader into the ...
Knapp的椭圆曲线基本看完了,于是翻了一下这本。本书分两部分。前半部分以古老的同余数问题为例子,主要介绍了 y^2= x^3-n^2x 这类椭圆曲线, 基本把它的一切都算清楚了。但遗憾的是,书中的计算只能是对某些特殊类型的椭圆曲线成立,椭圆曲线的基本性理论基本没怎么介绍;例如CM类型的椭圆曲线,其对应着某代数数...
This chapter provides an algebraic introduction of addition operations on elliptic curves. Algebraic solutions are provided to calculate addition operations by dividing the problem into 4 cases: two symmetric points, one infinity point, two identical poi
This textbook covers the basic properties of elliptic curves and modular forms, with emphasis on certain connections with number theory. The ancient "congruent number problem" is the central motivating example for most of the book. My purpose is to make the subject accessible to those who find ...
be built up from I1(Z) and functions of the form I1(Mz). The q-expansion in (2.37) is one of the famous series in number theory. Its coefficients are denoted ten) and called the Ramanujan function of n, since it was Ramanujan who proved or conjectured many of their properties: 00...
INTRODUCTION TO ELLIPTIC CURVES AND MODULAR FORMS (Graduate Texts in Mathematics, 97)doi:10.1112/blms/18.2.213Scholl, A. JOxford University PressBulletin of the London Mathematical Society
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INTRODUCTION TO ELLIPTIC CURVES AND MODULAR FORMS (Graduate Texts in Mathematics, 97) The theory of elliptic curves and modular forms provides a fruitful meeting ground for such diverse areas as number theory, complex analysis, algebraic geo... A Scholl - 《Bulletin of the London Mathematical Soci...
If you want to know why the computations are correct, please read Silverman's text:Rational Points on Elliptic Curves. ECC mod p Definition.Let $$p > 3$$ be prime. The elliptic curve $$y^2 = x^3 + ax + b$$ over $$ℤ_p$$ is the set of solutions $$(x, y) \in ℤ_p...