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As evidence, many provided Ramanujan's τ(p) (case of weight 12). The only solutions up to 10 10 to the equation τ(p) ≡ 0 (mod p) are 2, 3, 5, 7, 2411, and 7 758 337 633 (sequence A007659 in the OEIS). [11] Lehmer (1947) conjectured that τ(n) ≠ 0 for all n, an assertion sometimes known as Lehmer's conjecture.
Later the Geometry Center at the University of Minnesota sold a loosely bound copy of the notes. In 2002, Sheila Newbery typed the notes in TeX and made a PDF file of the notes available, which can be downloaded from MSRI using the links below. The book (Thurston 1997) is an expanded version of the first three chapters of the notes. In 2022 the ...
In geometry, an arrangement of lines is the subdivision of the Euclidean plane formed by a finite set of lines. An arrangement consists of bounded and unbounded convex polygons , the cells of the arrangement, line segments and rays , the edges of the arrangement, and points where two or more lines cross, the vertices of the arrangement.
Formally the set of all Wilson loops forms an overcomplete basis of solutions to the Gauss' law constraint. The set of all Wilson lines is in one-to-one correspondence with the representations of the gauge group. This can be reformulated in terms of Lie algebra language using the weight lattice of the gauge group .
Lecture Notes in Mathematics is a book series in the field of mathematics, including articles related to both research and teaching. It was established in 1964 and was edited by A. Dold, Heidelberg and B. Eckmann, Zürich.
Biju Patnaik University of Technology (BPUT) is a public state university located in Rourkela, Odisha, India. It was established on 21 November 2002 and named after Biju Patnaik , a former Chief Minister of Odisha .
The 't Hooft loop is a disorder operator since it creates singularities in the gauge field, with their expectation value distinguishing the disordered phase of pure Yang–Mills theory from the ordered confining phase.
[12]: 24 This observation can be restated in category theoretic terms as the existence of a forgetful functor from groups to pointed sets. [12]: 582 A pointed set may be seen as a pointed space under the discrete topology or as a vector space over the field with one element. [13]
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