On "mixed" modular equations of degree 21

2020/05/30 by Chandankumar, S.
#11F20 #33E05 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2006.01122

Abstract

In the proposed work, we establish a total of six new P--Q modular equations involving theta--function f(-q) with moduli of orders 1, 3, 7 and 21.These equations can be regarded as modular identities in the alternate theory of signature 3. As a consequence, several values of quotients of theta--function are evaluated.

Related

• P--Q "mixed" modular equations of degree 15
• Modular equations of order p and Theta functions
• The explicit evaluations of Ramanujan's remarkable product of theta-functions a_{m, n}
• Applications of a new P-Q modular equation of degree two
• Series for 1/π of signature 20