Triple convolution of Ramanujan sums and applications

Key Points

• To provide a combinatorial proof for the limit theorem regarding triple convolutions of Ramanujan sums.
• Presented a combinatorial proof of the limit theorem.
• Compared with earlier proofs using exponential sums theory.
• Explored applications related to arithmetical functions.
• Confirmed the limit theorem for triple convolutions of Ramanujan sums.
• Demonstrated relevance to the study of specific arithmetical functions.