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- W3189207910 abstract "Let $eta>0$ be a fixed positive number, let $N$ be a sufficiently large number. In this paper, we study the second moment of the sum of Hecke eigenvalues over primes in short intervals (whose length is $eta log N$) on average (with some weights) over the family of weight $k$ holomorphic Hecke cusp forms. We also generalize the above result to Hecke-Maass cusp forms for $SL(2,mathbb{Z})$ and $SL(3,mathbb{Z}).$ By applying the Hardy-Littlewood prime 2-tuples conjecture, we calculate the exact values of the mean values." @default.
- W3189207910 created "2021-08-16" @default.
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- W3189207910 date "2021-08-10" @default.
- W3189207910 modified "2023-09-23" @default.
- W3189207910 title "On sum of Hecke eigenvalue squares over primes in very short intervals" @default.
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- W3189207910 doi "https://doi.org/10.48550/arxiv.2108.04968" @default.
- W3189207910 hasPublicationYear "2021" @default.
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