Zobrazeno 1 - 10
of 28
pro vyhledávání: '"Rizwanur Khan"'
Autor:
Rizwanur Khan, Zeyuan Zhang
Publikováno v:
Mathematika. 69:573-583
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::8cfc171e94641c0c97267d67ed9c0d76
https://doi.org/10.1112/mtk.12199
https://doi.org/10.1112/mtk.12199
Publikováno v:
Journal of Number Theory. 239:1-20
Let ω ( n ) denote the number of distinct prime factors of n and let τ k ( n ) denote the k-fold divisor function. Adapting a method of Granville and Soundararajan, we evaluate the centralized moments of ω ( n ) , weighted by τ k ( n ) , and dedu
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::73d50dd6b26670dad195ae7b78b822f4
https://doi.org/10.1016/j.jnt.2021.10.010
https://doi.org/10.1016/j.jnt.2021.10.010
Autor:
Rizwanur Khan
Publikováno v:
Transactions of the American Mathematical Society. 375:6769-6796
We prove hybrid subconvexity bounds for twisted L L -functions L ( s , f × χ ) L(s,f\times \chi ) at the central point using a fourth moment estimate, including a new instance of the Burgess subconvexity bound.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::7a16b312f311c59a58aa39b19cf5ab08
https://doi.org/10.1090/tran/8647
https://doi.org/10.1090/tran/8647
Autor:
RIZWANUR KHAN, MATTHEW P. YOUNG
Publikováno v:
Journal of the Institute of Mathematics of Jussieu. :1-45
We establish sharp bounds for the second moment of symmetric-square L-functions attached to Hecke Maass cusp forms $u_j$ with spectral parameter $t_j$ , where the second moment is a sum over $t_j$ in a short interval. At the central point $s=1/2$ of
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::9843213634615d1274c0b29829ac355d
https://doi.org/10.1017/s1474748021000566
https://doi.org/10.1017/s1474748021000566
Publikováno v:
Mathematische Zeitschrift
We show that for at least $\frac{5}{13}$ of the primitive Dirichlet characters $\chi$ of large prime modulus, the central value $L(\frac{1}{2},\chi)$ does not vanish, improving on the previous best known result of $\frac{3}{8}$.
Comment: Improve
Comment: Improve
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::768391f87f034d0cd3f984ffa94fd03e
https://doi.org/10.1007/s00209-021-02821-8
https://doi.org/10.1007/s00209-021-02821-8
Autor:
Rizwanur Khan
Publikováno v:
The Quarterly Journal of Mathematics. 72:1133-1145
We prove hybrid subconvexity bounds for a wide class of twisted L-functions L(s, f × χ) at the central point, including a new instance of the Weyl subconvexity bound.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::65848e99bf7ebfe463c010c15a785a0d
https://doi.org/10.1093/qmath/haaa069
https://doi.org/10.1093/qmath/haaa069
Autor:
Rizwanur Khan, Peter Humphries
Publikováno v:
Geometric and Functional Analysis. 30:34-125
We prove two results on arithmetic quantum chaos for dihedral Maass forms, both of which are manifestations of Berry's random wave conjecture: Planck scale mass equidistribution and an asymptotic formula for the fourth moment. For level $1$ forms, th
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::ee66c7b2038672c8ce9dd02b5dd2cdb7
https://doi.org/10.1007/s00039-020-00526-4
https://doi.org/10.1007/s00039-020-00526-4
Autor:
Rizwanur Khan, Valentin Blomer
Publikováno v:
Journal of Functional Analysis. 276:2315-2358
A non-symmetric reciprocity formula is established that expresses the fourth moment of automorphic L-functions of level q and primitive central character twisted by the l-th Hecke eigenvalue as a twisted mixed moment of automorphic L-functions of lev
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::cd5dbf22239b8dd0e7bab5bc319b19d4
https://doi.org/10.1016/j.jfa.2018.11.009
https://doi.org/10.1016/j.jfa.2018.11.009
Autor:
Rizwanur Khan, Soumya Das
Publikováno v:
The Quarterly Journal of Mathematics. 69:1063-1087
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::0561b3b8cc3b47bd3069b0c3d2e357ef
https://doi.org/10.1093/qmath/hay012
https://doi.org/10.1093/qmath/hay012
Autor:
Jack Buttcane, Rizwanur Khan
Publikováno v:
Compositio Mathematica. 153:1479-1511
Conditionally on the generalized Lindelöf hypothesis, we obtain an asymptotic for the fourth moment of Hecke–Maass cusp forms of large Laplacian eigenvalue for the full modular group. This lends support to the random wave conjecture.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2bc5e91654b8c5b439e1cd02d8fbff84
https://doi.org/10.1112/s0010437x17007199
https://doi.org/10.1112/s0010437x17007199