math-notes

TeXed notes for personal study. Comments are welcome!

For web, use this link: here

List of notes:

• Number theory
  • Proof of $L(2, \chi_{-3}) \not \in \mathbb{Q}$ by Calegari-Dimitrov-Tang
  • Modular forms on $G_2$
  • Automorphic forms on GL(2)
  • Structure of $(\mathbb{Z}/p^{n}\mathbb{Z})^{\times}$
  • Nontrivial examples of ideal class groups
  • Hilbert’s theorem 90
  • Some properties of $p$-adic numbers
  • Automorphic induction from GL(1) to GL(2)
  • Irrationality measure
  • Unramified extension of $\mathbb{Q}(\sqrt{3})$
  • Langlands functoriality (ongoing)
• Geometry
  • Singular algebraic curves (follow Chapter 4 of Serre’s Algebraic Groups and Class fields)
  • $\mathbb{S}^2$ is not a Lie group
  • Low-dimensional complex Spin groups
• Representation theory
  • Littlewood-Richardson rule (ongoing)
• Miscellaneous
  • Similarity of matrices and field extension
  • Probabilities in poker game

Re-TeXed articles

I re-TeXed some of the existing articles with old typesets or non-English (e.g. French) for my own study. Let me know if there are any issues, errors, or possible improvements.

• I. Piatetski-Shapiro, Work of Waldspurger, Lie group representations, II (College Park, Md., 1982/1983), 280–302. Lecture Notes in Math., 1041 Springer-Verlag, Berlin, 1984

• R. Beuzart-Plessis, PROGRÈS RÉCENTS SUR LES CONJECTURES DE GAN-GROSS-PRASAD (d’après Jacquet-Rallis, Waldspurger, W. Zhang, etc.). Séminaire BOURBAKI (2018): 70e.

• J. Bourgain, L. Clozel, J-P. Kahane, Principe d’Heisenberg et fonctions positives, Annales de l’institut Fourier, Tome 60, no 4 (2010), p. 1215-1232.

• J-P. Labesse, L-indistinguishable representations and trace formula for SL(2), Lie Groups and their Representations (I. M. Gelfand, ed.), Wiley, New York, 1975.

• F. Beukers, Irrationality proofs using modular forms, Astérisque, tome 147-148 (1987), p. 271-283