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Research Output 2007 2019

  • 87 Citations
  • 5 h-Index
  • 19 Article
2019
1 Citation (Scopus)

Twisted moments of L-functions and spectral reciprocity

Blomer, V. & Khan, R., 1 Jan 2019, In : Duke Mathematical Journal. 168, 6, p. 1109-1177 69 p.

Research output: Contribution to journalArticle

Reciprocity
L-function
Moment
Eigenvalue
Corollary
2018
1 Citation (Scopus)

A conjecture for the regularized fourth moment of Eisenstein series

Djanković, G. & Khan, R., 1 Jan 2018, In : Journal of Number Theory. 182, p. 236-257 22 p.

Research output: Contribution to journalArticle

Eisenstein Series
L-function
Moment
Moment Problem
Asymptotic Formula

The fifth moment of Hecke L -functions in the weight aspect

Khan, R., 1 Jan 2018, (Accepted/In press) In : Mathematical Proceedings of the Cambridge Philosophical Society.

Research output: Contribution to journalArticle

Cusp Form
L-function
Upper bound
Moment
Eigenvalue

The third moment of symmetric square L-functions

Das, S. & Khan, R., 1 Sep 2018, In : Quarterly Journal of Mathematics. 69, 3, p. 1-25 25 p.

Research output: Contribution to journalArticle

Cusp Form
L-function
Moment
1 Citation (Scopus)

Uniform subconvexity and symmetry breaking reciprocity

Blomer, V. & Khan, R., 1 Jan 2018, (Accepted/In press) In : Journal of Functional Analysis.

Research output: Contribution to journalArticle

Reciprocity
L-function
Symmetry Breaking
Moment
Eigenvalue
2017
3 Citations (Scopus)

A mean value of a triple product of L-functions

Buttcane, J. & Khan, R., 1 Feb 2017, In : Mathematische Zeitschrift. 285, 1-2, p. 565-591 27 p.

Research output: Contribution to journalArticle

Triple product
L-function
Mean Value
Norm
Power Saving
2 Citations (Scopus)

On the fourth moment of Hecke-Maass forms and the random wave conjecture

Buttcane, J. & Khan, R., 1 Jul 2017, In : Compositio Mathematica. 153, 7, p. 1479-1511 33 p.

Research output: Contribution to journalArticle

Laplacian Eigenvalues
Cusp Form
Modular Group
Largest Eigenvalue
Moment
2016
1 Citation (Scopus)

Nonvanishing of Dirichlet L-functions

Khan, R. & Ngo, H. T., 2016, In : Algebra and Number Theory. 10, 10, p. 2081-2091 11 p.

Research output: Contribution to journalArticle

Dirichlet L-function
Dirichlet Character
Vanish
Modulus
5 Citations (Scopus)

The divisor function in arithmetic progressions modulo prime powers

Khan, R., 2016, In : Mathematika. 62, 3, p. 898-908 11 p.

Research output: Contribution to journalArticle

Divisor Function
Arithmetic sequence
Modulo
Odd
Integer
2015
2 Citations (Scopus)

L4-norms of Hecke newforms of large level

Buttcane, J. & Khan, R., 23 Nov 2015, In : Mathematische Annalen. 362, 3-4, p. 699-715 17 p.

Research output: Contribution to journalArticle

L-function
Mean Value
Upper bound
Norm
Estimate
1 Citation (Scopus)

On the subconvexity problem for GL(3) × GL(2) L-functions

Khan, R., 1 Mar 2015, In : Forum Mathematicum. 27, 2, p. 897-913 17 p.

Research output: Contribution to journalArticle

Sum of squares
Fourier coefficients
L-function
Lower bound
Form
1 Citation (Scopus)

Simultaneous nonvanishing of Dirichlet L-functions and twists of Hecke-Maass L-functions

Das, S. & Khan, R., 1 Sep 2015, In : Journal of the Ramanujan Mathematical Society. 30, 3, p. 237-250 14 p.

Research output: Contribution to journalArticle

Dirichlet Character
Dirichlet L-function
L-function
Conductor
Twist
2014

On the fourth moment of holomorphic Hecke cusp forms

Khan, R., 2014, In : Ramanujan Journal. 34, 1, p. 83-107 25 p.

Research output: Contribution to journalArticle

Cusp Form
Moment
Interval
2013
33 Citations (Scopus)

Distribution of mass of holomorphic cusp forms

Blomer, V., Khan, R. & Young, M., 1 Nov 2013, In : Duke Mathematical Journal. 162, 14, p. 2609-2644 36 p.

Research output: Contribution to journalArticle

Cusp Form
L-function
Siegel Modular Forms
Norm
Mean Value
2012
6 Citations (Scopus)

Simultaneous non-vanishing of GL(3) × GL(2) and GL(2) L-functions

Khan, R., May 2012, In : Mathematical Proceedings of the Cambridge Philosophical Society. 152, 3, p. 535-553 19 p.

Research output: Contribution to journalArticle

L-function
Form
Family
2010
16 Citations (Scopus)

Non-vanishing of the symmetric square L-function at the central point

Khan, R., May 2010, In : Proceedings of the London Mathematical Society. 100, 3, p. 736-762 27 p.

Research output: Contribution to journalArticle

L-function
Proportion
Strip
Vanish
Symmetry
1 Citation (Scopus)

Spacings between integers having typically many prime factors

Khan, R., Mar 2010, In : Canadian Mathematical Bulletin. 53, 1, p. 102-117 16 p.

Research output: Contribution to journalArticle

Prime factor
Spacing
Integer
Poisson distribution
Poisson process
2009
4 Citations (Scopus)

The second moment of dirichlet twists of hecke L-functions

Gao, P., Khan, R. & Ricotta, G., 2009, In : Acta Arithmetica. 140, 1, p. 57-65 9 p.

Research output: Contribution to journalArticle

L-function
Twist
Dirichlet
Moment
2007
9 Citations (Scopus)

The first moment of the symmetric-square L-function

Khan, R., Jun 2007, In : Journal of Number Theory. 124, 2, p. 259-266 8 p.

Research output: Contribution to journalArticle

L-function
Moment
Modular Group
Line
Corollary