This quantity is the 1st of 3 in a sequence surveying the idea of theta features. in accordance with lectures given through the writer on the Tata Institute of primary learn in Bombay, those volumes represent a scientific exposition of theta services, starting with their ancient roots as analytic services in a single variable (Volume I), concerning many of the appealing methods they are often used to explain moduli areas (Volume II), and culminating in a methodical comparability of theta capabilities in research, algebraic geometry, and illustration thought (Volume III).
Read or Download Tata Lectures on Theta I (Modern Birkhäuser Classics) PDF
Best Algebraic Geometry books
Fractal styles have emerged in lots of contexts, yet what precisely is a development? How can one make unique the buildings mendacity inside items and the relationships among them? This ebook proposes new notions of coherent geometric constitution to supply a clean method of this popular box. It develops a brand new inspiration of self-similarity referred to as "BPI" or "big items of itself," which makes the sphere a lot more straightforward for individuals to go into.
The idea of elliptic curves is amazing via its lengthy background and through the variety of the tools which have been utilized in its learn. This booklet treats the mathematics process in its glossy formula, by using uncomplicated algebraic quantity conception and algebraic geometry. Following a short dialogue of the mandatory algebro-geometric effects, the publication proceeds with an exposition of the geometry and the formal workforce of elliptic curves, elliptic curves over finite fields, the complicated numbers, neighborhood fields, and international fields.
This e-book introduces the speculation of modular varieties, from which all rational elliptic curves come up, with a watch towards the Modularity Theorem. dialogue covers elliptic curves as complicated tori and as algebraic curves; modular curves as Riemann surfaces and as algebraic curves; Hecke operators and Atkin-Lehner idea; Hecke eigenforms and their mathematics homes; the Jacobians of modular curves and the Abelian forms linked to Hecke eigenforms.
Additional resources for Tata Lectures on Theta I (Modern Birkhäuser Classics)