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Mathematical Proceedings of the Cambridge Philosophical Society, ISSN 0305-0041, 2018, Volume 168, Issue 3, pp. 543 - 566
We prove an upper bound for the fifth moment of Hecke L-functions associated to holomorphic Hecke cusp forms of full level and weight k in a dyadic interval K... 
2010 Mathematics Subject Classification | 11M99 (Secondary) | 11F03 (Primary) | 11F03 | MATHEMATICS | 11M99 | BOUNDS | COEFFICIENTS | VALUES | MAASS FORMS | Eigenvalues | Upper bounds | Weight
Journal Article
Forum Mathematicum, ISSN 0933-7741, 03/2015, Volume 27, Issue 2, pp. 897 - 913
Fix a self-dual Hecke–Maass form for SL (ℤ). Let be a holomorphic newform of prime level and fixed weight. Conditional on a lower bound for a short sum of... 
functions | 11M99 | subconvexity | L-functions
Journal Article
Mathematische annalen, ISSN 1432-1807, 2018, Volume 373, Issue 1-2, pp. 287 - 353
Using a cubic moment, we prove a Weyl-type subconvexity bound for the quadratic twists of a holomorphic newform of square-free level, trivial nebentypus, and... 
Mathematics, general | Mathematics | 11F37 | 11M99 | 11F11 | 11F66 | MATHEMATICS | FOURIER COEFFICIENTS | Mathematics - Number Theory
Journal Article
Monatshefte für Mathematik, ISSN 1436-5081, 2016, Volume 182, Issue 4, pp. 957 - 975
In this paper, we discuss the analytic representations of q-Euler sums which involve q-harmonic numbers through q-polylogarithms, either linearly or... 
65B10 | 33B15 | 05A30 | 11M99 | 11M32 | q-Riemann zeta function | Mathematics, general | Mathematics | 11M06 | q-Polylogarithm function | q-Euler sums | 33D05 | MATHEMATICS | ZETA-FUNCTIONS | INTEGRAL-REPRESENTATIONS
Journal Article
Functiones et Approximatio, Commentarii Mathematici, ISSN 0208-6573, 12/2015, Volume 53, Issue 2, pp. 249 - 304
We estimate the sum of products or quotients of L-functions, where the sum is taken over all quadratic extensions of given genus over a fixed global function... 
L-functions | Function fields | function fields | 11G40 | 11M99 | 11G20
Journal Article
Duke Mathematical Journal, ISSN 0012-7094, 02/2009, Volume 146, Issue 3, pp. 401 - 448
We study the average size of shifted convolution summation terms related to the problem of quantum unique ergodicity (QUE) on SL2(Z)\H. Establishing an... 
MATHEMATICS | COEFFICIENTS | POWERS | 11M99 | 11N36 | 11F30
Journal Article
The Ramanujan Journal, ISSN 1382-4090, 5/2018, Volume 46, Issue 1, pp. 91 - 102
With the help of transformation formulas of Dirichlet L-series, we generalize some classical formulas for the values $$\zeta (2N+1)$$ ζ(2N+1) given by... 
Dirichlet L -functions | Fourier Analysis | Eichler integral | 11M99 | Functions of a Complex Variable | Infinite series | Field Theory and Polynomials | Mathematics | Number Theory | Combinatorics | Mellin transform | Dirichlet L-functions | MATHEMATICS | EICHLER INTEGRALS
Journal Article
The Ramanujan Journal, ISSN 1382-4090, 5/2018, Volume 46, Issue 1, pp. 77 - 89
This paper introduces a new constant $$\kappa $$ κ , with a definition closely related to that of the Euler–Mascheroni’s constant $$\gamma $$ γ . Some... 
Euler–Mascheroni constant | Fourier Analysis | 11M99 | Functions of a Complex Variable | Field Theory and Polynomials | Zeta function | Mathematics | Number Theory | Combinatorics | Gamma function | Classical analysis | MATHEMATICS | Euler-Mascheroni constant | DOUBLE INTEGRALS
Journal Article
Annals of combinatorics, ISSN 0219-3094, 2015, Volume 19, Issue 3, pp. 513 - 543
In this paper we obtain precise asymptotics for certain families of graphs, namely circulant graphs and degenerating discrete tori. The asymptotics contain... 
58J52 | 11M99 | zeta functions | 05C30 | circulant graphs | Mathematics | 33A40 | Combinatorics | spanning trees | Bessel functions | BESSEL-FUNCTIONS | MATHEMATICS, APPLIED | HEAT KERNELS | ZETA-FUNCTIONS | FORMULAS | CHEBYSHEV POLYNOMIALS | CYCLE | Mathematics - Combinatorics
Journal Article
The Ramanujan journal, ISSN 1572-9303, 2015, Volume 42, Issue 2, pp. 479 - 489
The aim of this paper is to study certain multiple series which can be regarded as multiple analogues of Eisenstein series. As part of a prior research, the... 
Fourier Analysis | 11M41 | Multiple Eisenstein series | 11M99 | Functions of a Complex Variable | Field Theory and Polynomials | Riemann zeta function | Mathematics | Number Theory | Hyperbolic functions | Combinatorics | Lemniscate constant | MATHEMATICS
Journal Article
Monatshefte für Mathematik, ISSN 0026-9255, 2/2013, Volume 169, Issue 2, pp. 127 - 143
Under the generalized Lindelöf Hypothesis in the t- and q-aspects, we bound exponential sums with coefficients of Dirichlet series belonging to a certain... 
11M99 | Mathematics, general | Mathematics | Dirichlet series | 11F30 | 11L07 | Piatetski–Shapiro primes | Exponential sums | Hecke eigenvalues | 11F11 | Piatetski-Shapiro primes | MATHEMATICS
Journal Article
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, ISSN 1865-8784, 2014, Volume 85, Issue 1, pp. 53 - 57
Let $$\widetilde{f}$$ f ~ be an $$L^2$$ L 2 -normalized holomorphic dihedral form of prime level $$q$$ q and fixed weight. We show that, for any $$\varepsilon... 
Geometry | Dihedral form | Algebra | 11M99 | Mathematics, general | Mathematics | Number Theory | Topology | Differential Geometry | L^4$$ L 4 -norm | Grossencharacter | 11F11
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 12/2012, Volume 396, Issue 1, pp. 199 - 214
For any real a>0 we determine the supremum of the real σ such that ζ(σ+it)=a for some real t. For 01 the results turn out to be quite... 
Zeta function | LLL algorithm | Extreme values | MATHEMATICS | MATHEMATICS, APPLIED
Journal Article
The Ramanujan Journal, ISSN 1382-4090, 10/2015, Volume 38, Issue 1, pp. 129 - 145
Improving on a result by Luo, we prove that for $$K^{\frac{1}{3}}\le G\le K$$ K 1 3 ≤ G ≤ K , $$\begin{aligned} \sum _{\begin{array}{c} k\text { even}\\ K\le... 
Second moment | Fourier Analysis | 11M99 | Functions of a Complex Variable | Central value | Field Theory and Polynomials | Mathematics | Symmetric square L-functions | Average over Hecke basis | Number Theory | Combinatorics | Holomorphic cusp forms | Number theory | MATHEMATICS
Journal Article
Forum Mathematicum, ISSN 0933-7741, 07/2014, Volume 26, Issue 4, pp. 1071 - 1115
We consider certain double series of Eisenstein type involving hyperbolic-sine functions. We define certain generalized Hurwitz numbers, in terms of which we... 
11M41 | zeta functions | 11M99 | hyperbolic functions | Eisenstein series | lemniscate constant | Hurwitz numbers | Hyperbolic functions | Lemniscate constant | Q-zeta functions | MATHEMATICS | MATHEMATICS, APPLIED | q-zeta functions | EULER | Numbers | Mathematics - Number Theory
Journal Article
Functiones et Approximatio, Commentarii Mathematici, ISSN 0208-6573, 12/2015, Volume 53, Issue 1, pp. 97 - 122
Let f be a holomorphic cusp form of weight k with respect to the full modular group SL_2(\mathbb{Z}). We suppose that f is a normalized Hecke eigenform. Let... 
Derivative | Approximate functional equation | Cusp forms | Mean value formula | L-functions | mean value formula | 11M99 | cusp forms | approximate functional equation | 11N99 | derivative
Journal Article
The American Mathematical Monthly, ISSN 0002-9890, 08/2018, Volume 125, Issue 7, pp. 593 - 601
For a fixed we say that a point (r, s) in the integer lattice is b-visible from the origin if it lies on the graph of a power function f(x) = ax b with and no... 
Primary 11P21 | Secondary 11M99 | MATHEMATICS | INTEGERS
Journal Article
The Ramanujan Journal, ISSN 1382-4090, 5/2015, Volume 37, Issue 1, pp. 79 - 88
In a recent paper Kachi and Tzermias give elementary proofs of four product formulas involving $$\zeta (3)$$ ζ ( 3 ) , $$\pi $$ π , and Catalan’s constant.... 
Generalized Euler constants | 33B99 | 11M99 | Functions of a Complex Variable | Catalan constant | Field Theory and Polynomials | Borwein–Dykshoorn function | Mathematics | Fourier Analysis | Zeta function | 11Y60 | 11M06 | Number Theory | Combinatorics | Glaisher–Kinkelin constant
Journal Article
Mathematische Annalen, ISSN 0025-5831, 10/2015, Volume 363, Issue 1-2, pp. 175 - 216
We derive a Motohashi-type formula for the cubic moment of central values of L L -functions of level q q 11F30 | 11F37 | 11M99 | 11F66 | Mathematics - Number Theory
Journal Article
Complex Analysis and Operator Theory, ISSN 1661-8254, 2/2012, Volume 6, Issue 1, pp. 237 - 255
We consider Dirichlet series $${\zeta_{g,\alpha}(s)=\sum_{n=1}^\infty g(n\alpha) e^{-\lambda_n s}}$$ for fixed irrational α and periodic functions g. We... 
Operator Theory | 30D99 | 11M99 | 33E20 | Analysis | Analytic continuation | Mathematics, general | Mathematics | Dirichlet series | MATHEMATICS | MATHEMATICS, APPLIED | Universities and colleges
Journal Article
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