2011, IAS/Park City mathematics series, ISBN 9780821853207, Volume 18, xiv, 499

Book

2011, Student mathematical library : IAS/Park City mathematical subseries, ISBN 0821852426, Volume 58, xiv, 195

Book

2015, 3rd edition., Graduate studies in mathematics, ISBN 9780821898543, Volume 163, xxiv, 629

Book

International Journal of Number Theory, ISSN 1793-0421, 02/2016, Volume 12, Issue 1, pp. 27 - 55

Let π j be a self-contragredient automorphic cuspidal representation of GL m j ( ℚ ) for j = 1 , … , k . Using a refined version of the Selberg orthogonality,...

Selberg orthogonality | zeros of L -functions | Automorphic L -functions | n -level correlation of zeros of L -functions | lower-order terms of n -level correlation of zeros of L -functions | MATHEMATICS | Automorphic L-functions | RATIOS CONJECTURE | 1-LEVEL DENSITY | PRIME NUMBER THEOREM | FAMILIES | EXTERIOR SQUARE | n-level correlation of zeros of L-functions | zeros of L-functions | FUNCTORIALITY | lower-order terms of n-level correlation of zeros of L-functions

Selberg orthogonality | zeros of L -functions | Automorphic L -functions | n -level correlation of zeros of L -functions | lower-order terms of n -level correlation of zeros of L -functions | MATHEMATICS | Automorphic L-functions | RATIOS CONJECTURE | 1-LEVEL DENSITY | PRIME NUMBER THEOREM | FAMILIES | EXTERIOR SQUARE | n-level correlation of zeros of L-functions | zeros of L-functions | FUNCTORIALITY | lower-order terms of n-level correlation of zeros of L-functions

Journal Article

Geometric and functional analysis, ISSN 1420-8970, 2015, Volume 25, Issue 2, pp. 453 - 516

We prove an asymptotic formula with a power saving error term for the (pure or mixed) second moment $$\underset{\chi \bmod {q}}{\left. \sum \right.^{\ast}}...

Secondary 11L07 | Primary 11F66 | summation formulae | Analysis | character twists | exponential sums | 11F72 | L -functions | Mathematics | Asymptotic formula | L-functions | EXPONENTIAL-SUMS | ELLIPTIC-CURVES | EQUIDISTRIBUTION | SQUARE | 4TH MOMENT | HYBRID BOUNDS | MATHEMATICS | AUTOMORPHIC L-FUNCTIONS | COEFFICIENTS | SELBERG L-FUNCTIONS | Energy conservation | Mathematics - Number Theory

Secondary 11L07 | Primary 11F66 | summation formulae | Analysis | character twists | exponential sums | 11F72 | L -functions | Mathematics | Asymptotic formula | L-functions | EXPONENTIAL-SUMS | ELLIPTIC-CURVES | EQUIDISTRIBUTION | SQUARE | 4TH MOMENT | HYBRID BOUNDS | MATHEMATICS | AUTOMORPHIC L-FUNCTIONS | COEFFICIENTS | SELBERG L-FUNCTIONS | Energy conservation | Mathematics - Number Theory

Journal Article

The Ramanujan Journal, ISSN 1382-4090, 4/2019, Volume 48, Issue 3, pp. 567 - 575

Hafner and Stopple proved a conjecture of Zagier on the asymptotic expansion of a Lambert series involving Ramanujan’s tau function with the main term...

Symmetric square L -function | Functions of a Complex Variable | Primary: 11M06 | Maass cusp form | Field Theory and Polynomials | Rankin–Selberg L -function | Mathematics | Secondary: 11F30 | Fourier Analysis | Asymptotic expansion | 11M26 | Number Theory | 11N37 | Combinatorics | Symmetric square L-function | Rankin–Selberg L-function | MATHEMATICS | Rankin-Selberg L-function

Symmetric square L -function | Functions of a Complex Variable | Primary: 11M06 | Maass cusp form | Field Theory and Polynomials | Rankin–Selberg L -function | Mathematics | Secondary: 11F30 | Fourier Analysis | Asymptotic expansion | 11M26 | Number Theory | 11N37 | Combinatorics | Symmetric square L-function | Rankin–Selberg L-function | MATHEMATICS | Rankin-Selberg L-function

Journal Article

Advances in Mathematics, ISSN 0001-8708, 07/2018, Volume 332, pp. 403 - 437

With the method of moments and the mollification method, we study the central L-values of GL(2) Maass forms of weight 0 and level 1 and establish a...

Maass forms | Mollifiers | L-functions | Nonvanishing | MATHEMATICS | AUTOMORPHIC L-FUNCTIONS | J(Q) | DIRICHLET L-FUNCTIONS | RANK | ZEROS

Maass forms | Mollifiers | L-functions | Nonvanishing | MATHEMATICS | AUTOMORPHIC L-FUNCTIONS | J(Q) | DIRICHLET L-FUNCTIONS | RANK | ZEROS

Journal Article

International Journal of Number Theory, ISSN 1793-0421, 09/2011, Volume 7, Issue 6, pp. 1441 - 1461

We consider double L-functions with periodic coefficients and complex parameters. We prove functional equations for them, which is of traditional symmetric...

KubotaLeopoldt p-adic L-function | functional equation | Double L-function | Dirichlet L-function | POLYLOGARITHMS | MATHEMATICS | MULTIPLE ZETA-VALUES | HECKE L-FUNCTIONS | ANALYTIC CONTINUATION | Kubota-Leopoldt p-adic L-function | DIRICHLET L-FUNCTIONS | DOUBLE GAMMA | ASYMPTOTIC SERIES

KubotaLeopoldt p-adic L-function | functional equation | Double L-function | Dirichlet L-function | POLYLOGARITHMS | MATHEMATICS | MULTIPLE ZETA-VALUES | HECKE L-FUNCTIONS | ANALYTIC CONTINUATION | Kubota-Leopoldt p-adic L-function | DIRICHLET L-FUNCTIONS | DOUBLE GAMMA | ASYMPTOTIC SERIES

Journal Article

International Journal of Number Theory, ISSN 1793-0421, 08/2018, Volume 14, Issue 7, pp. 2045 - 2081

We consider the value distribution of the difference between logarithms of two symmetric power L -functions at s = σ > 1 / 2 . We prove that certain averages...

automorphic L -function | symmetric power L -function | Value-distribution | density function | automorphic L-function | symmetric power L-function | MATHEMATICS | ZETA-FUNCTION | L'/L

automorphic L -function | symmetric power L -function | Value-distribution | density function | automorphic L-function | symmetric power L-function | MATHEMATICS | ZETA-FUNCTION | L'/L

Journal Article

2011, 1st ed., ISBN 9788180303487, 4 v.

Book

International Journal of Number Theory, ISSN 1793-0421, 02/2018, Volume 14, Issue 1, pp. 289 - 299

Zagier’s conjecture on the asymptotic expansion of the Lambert series ∑ n = 1 ∞ τ 2 ( n ) exp ( − n z ) , where τ ( n ) is the Ramanujan’s tau function, was...

Rankin-Selberg L -function | cusp form | Asymptotic expansion | symmetric square L -function | MATHEMATICS | symmetric square L-function | Rankin-Selberg L-function

Rankin-Selberg L -function | cusp form | Asymptotic expansion | symmetric square L -function | MATHEMATICS | symmetric square L-function | Rankin-Selberg L-function

Journal Article

1995, Monographie CICMA lecture notes, Volume 1995-01, v, 185

Book

International Journal of Number Theory, ISSN 1793-0421, 08/2019, Volume 15, Issue 7, pp. 1487 - 1517

Let f be a fixed self-dual Hecke–Maass form for S L ( 3 , ℤ ) , and let u be an even Hecke–Maass form for S L ( 2 , ℤ ) with Laplace eigenvalue 1 / 4 + k 2 , k...

MATHEMATICS | MOMENT | GL | Rankin-Selberg L-function | subconvexity bound | Automorphic L-function | Voronoi formula | SELBERG L-FUNCTIONS | SUBCONVEXITY | CIRCLE METHOD

MATHEMATICS | MOMENT | GL | Rankin-Selberg L-function | subconvexity bound | Automorphic L-function | Voronoi formula | SELBERG L-FUNCTIONS | SUBCONVEXITY | CIRCLE METHOD

Journal Article

1989, Preprint / University of Toronto, Dept. of Mathematics, 25 leaves.

Book

Journal of Number Theory, ISSN 0022-314X, 02/2018, Volume 183, pp. 24 - 39

This is the second part of our investigation of mean values of derivatives of L-functions in function fields. In this paper, specifically, we prove several...

Random matrix theory | Quadratic Dirichlet L-functions | Derivatives of L-functions | Moments of L-functions | Function fields | MATHEMATICS

Random matrix theory | Quadratic Dirichlet L-functions | Derivatives of L-functions | Moments of L-functions | Function fields | MATHEMATICS

Journal Article

Journal of the European Mathematical Society, ISSN 1435-9855, 2017, Volume 19, Issue 5, pp. 1545 - 1576

Let q be odd and squarefree, and let chi(q) be the quadratic Dirichlet character of conductor q. Let u(j) be a Hecke-Maass cusp form on Gamma(0) (q) with...

Equidistribution | Subconvexity | Heegner points | L-functions | MATHEMATICS, APPLIED | DIRICHLET L-FUNCTIONS | CENTRAL VALUES | equidistribution | MAASS FORMS | MODULAR-FORMS | MATHEMATICS | AUTOMORPHIC L-FUNCTIONS | FOURIER COEFFICIENTS | HALF-INTEGRAL WEIGHT | CUSP FORMS | Mathematics - Number Theory

Equidistribution | Subconvexity | Heegner points | L-functions | MATHEMATICS, APPLIED | DIRICHLET L-FUNCTIONS | CENTRAL VALUES | equidistribution | MAASS FORMS | MODULAR-FORMS | MATHEMATICS | AUTOMORPHIC L-FUNCTIONS | FOURIER COEFFICIENTS | HALF-INTEGRAL WEIGHT | CUSP FORMS | Mathematics - Number Theory

Journal Article

2014, Graduate studies in mathematics, ISBN 1470417065, Volume 160., xviii, 371 pages

Book

2016, Contemporary mathematics, ISBN 147041709X, Volume 664, viii, 376

Book

International Mathematics Research Notices, ISSN 1073-7928, 2015, Volume 2015, Issue 2, pp. 325 - 354

We show that the twisted second moments of the Riemann zeta function averaged over the arithmetic progression 1/2 + i(an+ b) with a> 0, b real, exhibits a...

MATHEMATICS | DIRICHLET L-FUNCTIONS | VALUES

MATHEMATICS | DIRICHLET L-FUNCTIONS | VALUES

Journal Article

2014, Advanced lectures in mathematics, ISBN 9781571462961, Volume 30., iii, 204 pages

Book

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