Advanced Analytic Number Theory, Part I: Ramification by Carlos J. Moreno

By Carlos J. Moreno

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However, not all practitioners of the AmericanAustrian School wrote books on their subject—the largest part of their contribution is contained in their lectures and articles. Vandiver and Gould collected card-files on articles about Bernoulli numbers; this work was continued by Karl Dilcher and made available on the Web. It is also possible that Carlitz was a student of Schwatt at University of Pennsylvania, Philadelphia. Carlitz was born in Philadelphia, and the two have worked on similar mathematical topics.

4. 5. 6. 7. Jacobi theta functions and elliptic functions of one variable. Riemann Theta functions of one or more variables or Abelian functions. Weierstraß elliptic functions and sigma functions. The Glaisher-Neville-School for Jacobi elliptic functions. The q -School. The Heine function School. The Weierstraß-Mellin School of Gamma functions and hypergeometric functions. 8. The Italian elliptic function School. School 1 is about the Jacobi theta functions, so called after the German mathematician Carl Gustav Jacob Jacobi.

Vandiver and Gould collected card-files on articles about Bernoulli numbers; this work was continued by Karl Dilcher and made available on the Web. It is also possible that Carlitz was a student of Schwatt at University of Pennsylvania, Philadelphia. Carlitz was born in Philadelphia, and the two have worked on similar mathematical topics. Schwatt, who became PhD in 1893 in Philadelphia, remained in this city during his whole career (1897–1928). We will come back to the q-analogues of the Schwatt formulas in Chapter 5, where q-Stirling numbers are discussed.

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