Abstract
<abstract><p>In this paper, we prove a prime number theorem in short intervals for the Rankin-Selberg $ L $-function $ L(s, \phi\times\phi) $, where $ \phi $ is a fixed dihedral Maass newform. As an application, we give a lower bound for the proportion of primes in a short interval at which the Hecke eigenvalues of the dihedral form are greater than a given constant.</p></abstract>
Publisher
American Institute of Mathematical Sciences (AIMS)
Reference22 articles.
1. A. A. Karatsuba, M. B. Nathanson, Basic analytic number theory, Berlin, Heidelberg: Springer, 1993. https://doi.org/10.1007/978-3-642-58018-5
2. J. Liu, Y. Ye, Perron's formula and the prime number theorem for automorphic $L$-functions, Pure Appl. Math. Q., 3 (2007), 481–497. https://doi.org/10.4310/PAMQ.2007.v3.n2.a4
3. Y. Motohashi, On sums of Hecke-Maass eigenvalues squared over primes in short intervals, J. London Math. Soc., 91 (2015), 367–382. https://doi.org/10.1112/jlms/jdu079
4. M. Coleman, A zero-free region for the Hecke $L$-functions, Mathematika, 37 (1990), 287–304. https://doi.org/10.1112/S0025579300013000
5. A. Sankaranarayanan, J. Sengupta, Zero-density estimate of $L$-functions attached to Maass forms, Acta Arith., 127 (2007), 273–284. https://doi.org/10.4064/aa127-3-5