A twist of the Gauss circle problem by holomorphic cusp forms

Acharya, Ratnadeep

doi:10.1007/s40993-021-00299-1

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2022

2024

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Cited by 6 publications

(3 citation statements)

References 14 publications

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“…His result was improved by Templier and Tsimerman [24]. For polynomials in more variables, Acharya [1] proved…”

Section: Introductionmentioning

confidence: 99%

Sum of the Fourier coefficients of SL(3,Z) Hecke Maass forms over quadratics

Himanshi

Singh

2023

Journal of Number Theory

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“…His result was improved by Templier and Tsimerman [24]. For polynomials in more variables, Acharya [1] proved…”

Section: Introductionmentioning

confidence: 99%

Sum of the Fourier coefficients of SL(3,Z) Hecke Maass forms over quadratics

Himanshi

Singh

2023

Journal of Number Theory

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“…where s, t ∈ Z, F not necessarily an eigenform and c 7 = c 7 (F, N ) vanishes in many (but not all) cases. Acharya [20] proved…”

Section: Introductionmentioning

confidence: 99%

Sum of the triple divisor function and Fourier coefficients of $SL(3,\mathbb{Z})$ Hecke-Maass forms over quadratics

Himanshi¹,

Singh²

2023

Preprint

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“…For a polynomial with more than one variable, the problem has been studied broadly for many arithmetic functions. A two-variables analogue of the sum studied in the work of Blomer [3], has been studied by Banarjee-Pandey [2] and Acharya [1]. More precisely, they studied the distribution of {λ f (q(a, b))} where q(x, y) = x 2 + y 2 , and obtained an estimate for the summatory function k,l∈Z k 2 +l 2 ≤X λ f (q(k, l)).…”

Section: Introductionmentioning

confidence: 99%

Deterministic comparison of Hecke eigenvalues at the primes represented by a binary quadratic form

Vaishya¹

2022

Int. J. Math.

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Let [Formula: see text] and [Formula: see text] be the normalized [Formula: see text]-Fourier coefficient of distinct Hecke eigenforms [Formula: see text] and [Formula: see text] of integral weight for the full modular group, respectively, and [Formula: see text] is a primitive integral positive-definite binary quadratic form of fixed discriminant [Formula: see text] with the class number [Formula: see text]. We establish a lower bound for the analytic density of the set [Formula: see text] for each fixed [Formula: see text] With the above notation, we also obtain a lower bound for the analytic density of the set [Formula: see text] for each fixed [Formula: see text] As a consequence, we obtain a deterministic criterion for the equality of two Hecke eigenforms.

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A twist of the Gauss circle problem by holomorphic cusp forms

Cited by 6 publications

References 14 publications

Sum of the Fourier coefficients of SL(3,Z) Hecke Maass forms over quadratics

Sum of the Fourier coefficients of SL(3,Z) Hecke Maass forms over quadratics

Sum of the triple divisor function and Fourier coefficients of $SL(3,\mathbb{Z})$ Hecke-Maass forms over quadratics

Deterministic comparison of Hecke eigenvalues at the primes represented by a binary quadratic form

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