Bombieri-type theorems for exponential sums over primes in short intervals and its application

We treat the estimate of mean value of exponential sums over primes in short intervals and obtain the related Bombieri-type theorems, which generalize the result of Liu and Zhan (Acta Arith LXXXII(3):197–227, 1997 ). Moreover, we present some application to the distribution of primes in the ternary...

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Veröffentlicht in:	The Ramanujan journal 2018-06, Vol.46 (2), p.525-544
1. Verfasser:	Yao, Yanjun
Format:	Artikel
Sprache:	eng
Schlagworte:	Combinatorics Field Theory and Polynomials Fourier Analysis Functions of a Complex Variable Intervals Mathematics Mathematics and Statistics Number Theory Quadratic forms Sums Theorems
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Zusammenfassung:	We treat the estimate of mean value of exponential sums over primes in short intervals and obtain the related Bombieri-type theorems, which generalize the result of Liu and Zhan (Acta Arith LXXXII(3):197–227, 1997 ). Moreover, we present some application to the distribution of primes in the ternary quadratic form in short intervals.
ISSN:	1382-4090 1572-9303
DOI:	10.1007/s11139-017-9918-1