By Phillip Griffiths

A entire, self-contained therapy providing common result of the idea. Establishes a geometrical instinct and a operating facility with particular geometric practices. Emphasizes functions throughout the learn of attention-grabbing examples and the improvement of computational instruments. insurance levels from analytic to geometric. Treats simple concepts and result of complicated manifold conception, targeting effects acceptable to projective forms, and contains dialogue of the speculation of Riemann surfaces and algebraic curves, algebraic surfaces and the quadric line complicated in addition to detailed subject matters in complicated manifolds.

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Mod. Phys. A 15, 725–754 (2000). [hep-ph/9905237] 28. : Nested sums, expansion of transcendental functions and multiscale multiloop integrals. J. Math. Phys. 43, 3363–3386 (2002). [hep-ph/0110083] 29. : Analytic and algorithmic aspects of generalized harmonic sums and polylogarithms. 0378 [math-ph]] 30. : Harmonic sums and polylogarithms generated by cyclotomic polynomials. J. Math. Phys. 52, 102301 (2011). 6063 [math-ph]] 31. : High precision "-expansions of massive four loop vacuum bubbles Phys.

Phys. Commun. 174, 222–240 (2006). [hep-ph/0507152] 58. : DESY 13-064 Harmonic Sums, Polylogarithms, Special Numbers, and Their Generalizations 29 59. : The theory of deeply inelastic scattering. Prog. Part. Nucl. Phys. 69, 28 (2013). 6087 [hep-ph]] 60. : Structural relations of harmonic sums and Mellin transforms at weight w D 6. , Rosenberg, S. ) Motives, Quantum Field Theory, and Pseudodifferential Operators, vol. 12, pp. 167–186. Clay Mathematics Proceedings, American Mathematical Society (2010).

Phys. Commun. 133, 76–104 (2000). : Analytic continuation of the harmonic sums for the 3-loop anomalous dimensions. Phys. Lett. B 614, 53–61 (2005). [hep-ph/0503188] 119. : Analytic continuation of the Mellin moments of deep inelastic structure functions. [hep-ph/0501274] 120. : DESY Annual Report (2013) Multiple Zeta Values and Modular Forms in Quantum Field Theory David Broadhurst Abstract This article introduces multiple zeta values and alternating Euler sums, exposing some of the rich mathematical structure of these objects and indicating situations where they arise in quantum field theory.