Moments of the products of quadratic twists of automorphic L-functions

Sono, Keiju

doi:10.1007/s00229-016-0823-5

Cited by 6 publications

(3 citation statements)

References 15 publications

(17 reference statements)

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“…Nevertheless, a method of K. Soundararajan [27] with its refinement by A. J. Harper [7] provides a conditional approach towards establishing upper bounds for moments of L-functions under the generalized Riemann hypothesis (GRH). For families of quadratic twists of L-functions, such sharp upper bounds are obtained by K. Sono [24]. It follows from [24, Theorem 2.1] that for any real number k ≥ 0, we have under GRH,…”

Section: Introductionmentioning

confidence: 94%

Twisted first moment of quadratic and quadratic twist $L$-functions

Gao¹,

Zhao²

2023

Preprint

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Section: Introductionmentioning

confidence: 94%

Twisted first moment of quadratic and quadratic twist $L$-functions

Gao¹,

Zhao²

2023

Preprint

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“…Both methods work well in the case of more general class of L-functions. Some variations of these methods were applied to products of automorphic L-fucntions [22] and averages over fundmental discriminants of central values of quadratic twists [25].…”

Section: Moment Estimate Main Ideasmentioning

confidence: 99%

Variance estimates in Linnik's problem

Shubin¹

2021

Preprint

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We evaluate the variance of the number of lattice points in a small randomly rotated spherical ball on a surface of 3-dimensional sphere centered at the origin. Previously, Bourgain, Rudnick, and Sarnak showed conditionally on the Generalized Lindelöf Hypothesis that the variance is bounded from above by σ(Ω n )N n 1+ε , where σ(Ω n ) is the area of the ball Ω n on the unit sphere, N n is the total number of solutions of Diophantine equation x 2 + y 2 + z 2 = n. Assuming the Grand Riemann Hypothesis and using the moments method of Soundararajan and Harper, we establish the upper bound of the form cσ(Ω n )N n , where c is an absolute constant. This bound is of the conjectured order of magnitude.

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“…Soundararajan and Young [SY10] obtained second moments for quadratic twists of modular L-functions. Higher moments for products of automorphic L-functions are studied by Sono [Son16]. These results concern estimates of the order and error terms.…”

Section: Introductionmentioning

confidence: 99%

Explicit mean value theorems for toric periods and automorphic $L$-functions

Suzuki,

Wakatsuki

2021

Preprint

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Let F be a number field and D a quaternion algebra over F . Take a cuspidal automorphic representation π of D × A with trivial central character and a cusp form φ in π. Using the prehomogeneous zeta function, we find an explicit mean value of the toric periods of φ with respect to quadratic algebras over F . The result can also be written as a mean value formula for the central values of automorphic L-functions twisted by quadratic characters.

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Moments of the products of quadratic twists of automorphic L-functions

Abstract: In this paper, assuming the Generalized Riemann Hypothesis and some other hypotheses, we give sharp upper bounds for the moments of the products of central values of automorphic L-functions twisted by quadratic characters and averaged over fundamental discriminants.

Cited by 6 publications

References 15 publications

Twisted first moment of quadratic and quadratic twist $L$-functions

Twisted first moment of quadratic and quadratic twist $L$-functions

Variance estimates in Linnik's problem

Explicit mean value theorems for toric periods and automorphic $L$-functions

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