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Основанная на работах автора, эта монография является своеобразным введением в современную аналитическую теорию чисел. Первая глава монографии состоит из семи коротких статей на разные темы. Во второй главе изучаются аналитические свойства скалярных произведений L-рядов Артина — Вейля. Основная тема третьей главы — распределение целых точек на некоторых (естественных) целых моделях аффинных торических многообразий. В четвёртой главе доказаны две глубоких теоремы о представлении простых чисел полиномами третьей степени от двух переменных.
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