EXPLICIT EVALUATIONS OF TWO RAMANUJAN–SELBERG CONTINUED FRACTIONS

Liang-Cheng Zhang

doi:10.1142/s1793042105000297

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EXPLICIT EVALUATIONS OF TWO RAMANUJAN–SELBERG CONTINUED FRACTIONS

Liang-Cheng Zhang

Year: 2005 Journal: International Journal of Number Theory Vol: 01 (04)Pages: 593-601 Publisher: World Scientific

DOI: 10.1142/s1793042105000297

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Abstract

This paper gives explicit evaluations for two Ramanujan–Selberg continued fractions in terms of class invariants and singular moduli.

Keywords:

Mathematics Ramanujan's sum Selberg trace formula Pure mathematics Ramanujan tau function Moduli Class (philosophy) Algebra over a field Riemann hypothesis

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Advanced Mathematical Identities

Physical Sciences → Mathematics → Algebra and Number Theory

Analytic Number Theory Research

Physical Sciences → Mathematics → Algebra and Number Theory

Advanced Combinatorial Mathematics

Physical Sciences → Mathematics → Discrete Mathematics and Combinatorics

EXPLICIT EVALUATIONS OF TWO RAMANUJAN–SELBERG CONTINUED FRACTIONS

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