Number Theory

Eta Products and Theta Series Identities by Günter Köhler

Posted On March 23, 2017 at 10:46 am by / Comments Off on Eta Products and Theta Series Identities by Günter Köhler

By Günter Köhler

This monograph offers with items of Dedekind's eta functionality, with Hecke theta sequence on quadratic quantity fields, and with Eisenstein sequence. the writer brings to the general public the massive variety of identities which were found during the last twenty years, nearly all of that have no longer been released in other places. The publication may be of curiosity to graduate scholars and students within the box of quantity idea and, particularly, modular kinds. it's not an introductory textual content during this box. however, a few theoretical historical past fabric is gifted that's vital for realizing the examples partially II. partly I suitable definitions and crucial theorems -- corresponding to a whole evidence of the constitution theorems for coprime residue category teams in quadratic quantity fields that aren't simply obtainable within the literature -- are supplied. one other instance is a radical description of an set of rules for directory all eta items of given weight and point, including proofs of a few effects at the bijection among those eta items and lattice simplices.

Show description

Read or Download Eta Products and Theta Series Identities PDF

Best number theory books

Topological Vector Spaces

If you happen to significant in mathematical economics, you come back throughout this ebook many times. This booklet contains topological vector areas and in the community convex areas. Mathematical economists need to grasp those themes. This booklet will be an outstanding support for not just mathematicians yet economists. Proofs will not be demanding to stick to

Game, Set, and Math: Enigmas and Conundrums

A set of Ian Stewart's leisure columns from Pour los angeles technology, which show his skill to carry smooth maths to lifestyles.

Proceedings of a Conference on Local Fields: NUFFIC Summer School held at Driebergen (The Netherlands) in 1966

From July 25-August 6, 1966 a summer time tuition on neighborhood Fields was once held in Driebergen (the Netherlands), equipped through the Netherlands Universities origin for overseas Cooperation (NUFFIC) with monetary help from NATO. The medical organizing Committl! e consisted ofF. VANDER BLIJ, A. H. M.

Multiplicative Number Theory

The hot version of this thorough exam of the distribution of leading numbers in mathematics progressions bargains many revisions and corrections in addition to a brand new part recounting fresh works within the box. The publication covers many classical effects, together with the Dirichlet theorem at the life of top numbers in arithmetical progressions and the theory of Siegel.

Extra info for Eta Products and Theta Series Identities

Example text

9. A version of our proof was given in [120]; here we will choose another approach. The exponents am in an eta product of level N form vectors in a space of dimension τ (N ). 9) from the cones K(ps ) and simplices S(ps , k) for the prime powers ps dividing N . Therefore we begin with studying prime power levels. The compactness of K(ps ) will follow from an explicit description of the edges of K(ps ). We shall see that the cones and simplices grow larger when the primes get smaller (while the exponent s is fixed).

0 0 0 0 ... ... ... ... ...

An interesting class consists of those meromorphic modular forms whose poles are supported by the cusps, that is, which are holomorphic on H. Eta products belong to this class. The case of weight k = 0 is of foremost importance. A meromorphic modular form f of weight 0 and trivial multiplier system 1 for Γ is called a modular function for Γ. It satisfies f (Lz) = f (z) for all L ∈ Γ. Clearly, the set of all modular functions for Γ is a field. It can be identified with the field of meromorphic functions on the compact Riemann surface corresponding to Γ.

Download PDF sample

Rated 4.82 of 5 – based on 40 votes