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Intersection theory on Shimura surfaces II
Intersection theory Shimura surfaces II Number Theory
2012/3/1
This is the third of a series of papers relating intersections of special cycles on the integral model of a Shimura surface to Fourier coefficients of Hilbert modular forms. More precisely, we embed t...
Intersection theory on Shimura surfaces
Intersection theory Shimura surfaces intersection multiplicities
2012/3/1
Kudla has proposed a general program to relate arithmetic intersection multiplicities of special cycles on Shimura varieties to Fourier coefficients of Eisenstein series. The lowest dimensional case, ...
Some bounds and limits in the theory of Riemann's zeta function
bounds and limits theory of Riemann's zeta function Number Theory
2011/9/21
Abstract: For any real a>0 we determine the supremum of the real \sigma\ such that \zeta(\sigma+it) = a for some real t. For 0 < a < 1, a = 1, and a > 1 the results turn out to be quite different.}
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Abstract: This is the text from a talk at the Arbeitstagung 2011, which can serve as an introduction to arxiv:1009.0736 and arXiv:1007.0907. I first discuss how a global field is determined by a certa...
Diophantine Geometry over Groups X: The Elementary Theory of Free Products of Groups
Diophantine Geometry Groups X Elementary Theory of Free Products of Groups
2011/1/14
This paper is the 10th in a sequence on the structure of sets of solutions to systems of equations over groups, projections of such sets (Diophantine sets), and the structure of definable sets over fe...
The homotopy limit problem and (etale) hermitian K-theory
The homotopy limit problem hermitian K-theory
2010/11/24
Let X be a noetherian separated scheme with 2 invertible in the ring of regular functions. Assume further that $X$ has finite Krull dimension and there is a global bound on the virtual 2 cohomological...
Ramsey theory for words over a finite alphabet was unified in the work of Carlson and Furstenberg-Katznelson. Carlson, in the same work, outlined a method to extend the theory for words over an infin...
On a unified theory of numbers
unified theory numbers
2010/12/13
In 1873 James Clerk Maxwell combined electricity and magnetism using the Maxwell's Equations into a single force called electromagnetism and since then,physicists have been trying to discover the elus...
Inhomogeneous theory of dual Diophantine approximation on manifolds
Metric Diophantine approximation extremal manifolds
2010/12/14
The inhomogeneous Groshev type theory for dual Diophantine approximation on manifolds is developed. In particular, the notion of nice manifolds is introduced and the divergence part of the theory is e...
A crucial observation in Quillen’s definition of higher algebraic K-theory was
that the right way to proceed is to define the higer K-groups as the homotopy
groups of a space ([21]). Qui...
Cahit Arf's Contribution to Algebraic number Theory and Related Fields
Algebraic number Cahit Arf's Related Fields
2010/3/4
Cahit Arf's Contribution to Algebraic number Theory and Related Fields。