2024 Borcherds product

Borcherds product

Author: akwp

August undefined, 2024

WebJun 4, 2009 · La fonction [Phi]12 de Borcherds, forme modulaire en 26 variables pour le groupe orthogonal O+(II2,26) et le caractere determinant, de poids singulier 12, a ete construite par R.E.Borcherds en 1994 avec la theorie des produits automorphes. Elle determine la “Fake Monster Lie Algebra”, qui joue le role fondamental dans la preuve de … WebThese "Borcherds products" have infinite product expansions analogous to the Dedekind eta-function. They arise as multiplicative liftings of elliptic modular forms on $(SL)_2(R)$. The fact that the zeros and poles of Borcherds products are explicitly given in terms of Heegner divisors makes them interesting for geometric and arithmetic ...

Arithmetic cycles and automorphic forms - Department of …

WebApr 1, 2012 · We recast this result using the Borcherds–Harvey–Moore singular theta-lift and show that the vector-valued functions attached to completely replicable modular … WebApr 12, 2024 · Posted by Tom Leinster. Magnitude homology has been discussed extensively on this blog and definitely needs no introduction. A lot of questions about magnitude homology have been answered and a number of possible application have been explored up to this point, but magnitude homology was never exploited for the structure … round hill store

arXiv:math/0404427v1 [math.NT] 23 Apr 2004

WebSep 26, 2024 · In 1998, Borcherds [] created a remarkable method for constructing meromorphic modular forms on orthogonal groups of signature (2, n) from weakly holomorphic modular forms, and he showed that the Fourier expansions of such meromorphic modular forms at cusps have incredibly beautiful product representations … WebBorcherds products and their applications to arithmetic geometry May 3-10, 2009 ... The workshop is dedicated to Borcherds' theory concerning a singular theta lift from weakly holomorphic elliptic modular forms to automorphic forms on orthogonal groups which are forms of SO(2, n), and its applications and generalizations. A series of lectures ... WebThe Borcherds family name was found in the UK in 1891. In 1891 there was 1 Borcherds family living in Norfolk. This was 100% of all the recorded Borcherds's in United … stratos 476 sf fish and ski boat seats

A converse theorem for Borcherds products on $X_0(N)$

Web5. Borcherds products 37 6. Integral models 52 7. Normality and ﬂatness 72 8. Integral theory of q-expansions 84 9. Borcherds products on integral models 94 References … Webthe moonshine conjecture for the Conway group proposed by Borcherds [2,3] and Scheithauer [35,36]: all twists of the denominator identity of the fake monster Lie algebra … round hill soccer fieldWebApr 10, 2002 · These "Borcherds products" have infinite product expansions analogous to the Dedekind eta-function. They arise as … round hill swim lessons

"WebThe Fields Medal is a prize awarded to two, three, or four mathematicians under 40 years of age at the International Congress of the International Mathematical Union (IMU), a meeting that takes place every four years. The name of the award honours the Canadian mathematician John Charles Fields.. The Fields Medal is regarded as one of the highest … " - Borcherds product

Borcherds product

Borcherds Name Meaning & Borcherds Family History at

Webthe moonshine conjecture for the Conway group proposed by Borcherds [2,3] and Scheithauer [35,36]: all twists of the denominator identity of the fake monster Lie algebra by elements of Conway’s group Co 0 are the Fourier expansions of Borcherds products of singular weight on certain symmetric domains of type IV. It is well known that Sp WebOct 16, 2024 · Borcherds products are explained as solutions of a multiplicative Cousin problem, namely of finding a meromorphic functions with divisor supported on the …

Did you know?

WebAug 1, 2013 · Computing Borcherds products - Volume 16. To save this article to your Kindle, first ensure [email protected] is added to your Approved Personal … WebNov 23, 2024 · In particular, $G(\vartheta _R)$ is a Borcherds product. It turns out that this Borcherds product already appears in the work of Scheithauer [15, 17] and its expansion at a level 1 cusp is a twisted denominator identity of the fake monster algebra corresponding to an element g in Conway’s group ${\text {Co}}_0$.The theorem is proved by showing …

WebApr 1, 2012 · We recast this result using the Borcherds–Harvey–Moore singular theta-lift and show that the vector-valued functions attached to completely replicable modular functions with integer coefficients lift to automorphic functions with infinite product expansions at all cusps. ... Borcherds products." Duke Math. J. 161 (5) 893 - 950, 1 … WebSep 1, 2024 · The Borcherds lift Ψ N of ϕ N is then a (meromorphic) Borcherds product of weight 1/2. By a theorem of Bruinier ([3], Theorem 1.3) Ψ N is a quotient of two holomorphic Borcherds products; one of these is of half-integral weight. (Note that Borcherds products necessarily have either integral or half-integral weight by their definition.) Step 2.

WebJul 20, 2024 · Borcherds lift for an even lattice of signature (p,q) is a lifting from weakly holomorphic modular forms of weight (p-q)/2 for the Weil representation. We introduce a new product operation on the space of such modular forms and develop a basic theory. The product makes this space a finitely generated filtered associative algebra, without unit … WebBorcherds products Wednesdays from 9:15 to 10:45, INF 368, room 2481 The goal of the seminar is to understand the fundamental work of R. Borcherds on inﬁnite product expansions of holomorphic automorphic forms on certain orthogonal groups (resp. on Grassmannians). Probably the most prominent and well known example of product …

WebBorcherds products pdf: 8: Mar 18: Andrew: Heegner divisors and Borcherds products 9: Mar 25: Luis Garcia: Theta lifts and currents on Shimura varieties (special guest …

WebBORCHERDS PRODUCTS GYUJIN OH 1. Basic theory (Bruinier’s book) Here we give a crash course on the Borcherds products 8 <: Weakly holomorphic modular forms of … stratos 2 seaterWebWe prove that there are only finitely many isometry classes of even lattices of signature for which the space of cusp forms of weight for the Weil representation of the discriminant group of is trivial. We compute … stratos aerospace fort worthWebThe Borchers family name was found in the USA, the UK, Canada, and Scotland between 1840 and 1920. The most Borchers families were found in USA in 1920. In 1840 there … stratos 326xf specsWebJun 25, 2024 · A converse theorem for Borcherds products on. Jan Hendrik Bruinier, Markus Schwagenscheidt. We show that every Fricke invariant meromorphic modular … stratos aircraft management companyWebJul 20, 2024 · Quasi-pullback of Borcherds products is an operation of renormalized restriction. It produces a meromorphic modular form on a lower dimensional symmetric domain which is again a Borcherds product. roundhill swimming pool thurmastonWebarXiv:math/0404427v1 [math.NT] 23 Apr 2004 INFINITE PRODUCTS IN NUMBER THEORY AND GEOMETRY JAN HENDRIK BRUINIER Abstract. We give an introduction to the theory of Borcherds produc round hill swim teamWebMar 23, 2024 · Theta functions. Borcherds products. 1. Introduction. Infinite products appear in many places in number theory and combinatorics, for instance in the Euler … stratos 34 backpack