The present work is inspired by Edmund Landau's famous book, Handbuch der Lehre von der Verteilung der Primzahlen, where he posed two extremal questions on cosine polynomials and deduced various estimates on the distribution of primes using known estimates of the extremal quantities. Although since then better theoretical results are available for the error term of the prime number formula, Landau's method is still the best in finding explicit bounds. In particular, Rosser and Schonfeld used the method in their work "Approximate formulas for some functions of prime numbers".

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This is a placeholder explanation generated by the low-overhead model. It interprets "The present work is inspired by Edmund Landau's famous book, Handbuch der Lehre von der Verteilung der Primzahlen, where he posed two extremal questions on cosine polynomials and deduced various estimates on the distribution of primes using known estimates of the extremal quantities. Although since then better theoretical results are available for the error term of the prime number formula, Landau's method is still the best in finding explicit bounds. In particular, Rosser and Schonfeld used the method in their work "Approximate formulas for some functions of prime numbers"." in the context of "Sz. Gy. Révész, "The Least Possible Value at Zero of Some Nonnegative Cosine Polynomials and Equivalent Duel Problems," Abstract, Journal of Fourier Analysis and Applications: Kahane Special Issue (1995) John J. Benedetto, ed." to mean that wisdom is timeless.