Geodesic
Tur\'an Extremal Problem for Periodic Functions with Small Support and Its Applications
Matematičeskie zametki, Tome 76 (2004) no. 5, pp. 688-700.

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We study a Turán extremal problem on the largest mean value of a 1-periodic even function with nonnegative Fourier coefficients, fixed value at zero, and support on a closed interval $[-h,h]$, $0$. We show how the solution of this extremal problem for rational numbers $h=p/q$ is related to the solution of two finite-dimensional problems of linear programming. The solution of the Turán problem for rational numbers $h$ of the form $2/q$, $3/q$, $4/q$, is obtained. Applications of the Turán problem to analytic number theory are given. 
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D. V. Gorbachev; A. S. Manoshina. Tur\'an Extremal Problem for Periodic Functions with Small Support and Its Applications. Matematičeskie zametki, Tome 76 (2004) no. 5, pp. 688-700. http://geodesic.mathdoc.fr/item/MZM_2004_76_5_a4/

[1] Gorbachev D. V., Manoshina A. S., “Ekstremalnaya zadacha Turana dlya periodicheskikh funktsii s malym nositelem”, Chebyshevskii sb., T. 2, 2001, 31–40 | MR

[2] Manoshina A. S., “Ekstremalnaya zadacha Turana dlya funktsii s malym nositelem”, Izv. TulGU. Ser. matem., mekh., informatika, 6:3 (2000), 113–116

[3] Gorbachev D. V., Manoshina A. S., “Ekstremalnaya zadacha Turana dlya periodicheskikh funktsii s malym nositelem”, Tezisy dokl. IV Mezhdunarodnoi konferentsii “Sovremennye problemy teorii chisel i ee prilozheniya” (Tula, 2001), Izd-vo MGU, M., 2001, 45–46

[4] Stechkin S. B., “Odna ekstremalnaya zadacha dlya trigonometricheskikh ryadov s neotritsatelnymi koeffitsientami”, Stechkin S. B., Izbrannye trudy: Matematika, Nauka, M., 1998, 244–245

[5] Gorbachev D. V., “Ekstremalnaya zadacha dlya periodicheskikh funktsii s nositelem v share”, Matem. zametki, 69:3 (2001), 346–352 | MR | Zbl

[6] Bakhvalov N. S., Zhidkov N. P., Kobelkov G. M., Chislennye metody, Nauka, M., 1987 | Zbl

[7] Konyagin S., Shparlinski I., Character Sums with Exponential Functions and their Applications, Cambridge Univ. Press, Cambridge, 1999 | Zbl

[8] Montgomery H. L., Ten Lectures on the Interface between Analytic Number Theory and Harmonic Analysis, Amer. Math. Soc., Providence, RI, 1994