Sums of k-th powers and Fourier coefficients of cusp forms
In this paper, we will first establish a power saving result for the shifted convolution sums of k -th powers and the normalized Fourier coefficients of SL 2 ( Z ) cusp forms. Later we will generalize the result to higher rank cases.
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| Published in | The Ramanujan journal Vol. 60; no. 2; pp. 295 - 316 |
|---|---|
| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
New York
Springer US
01.02.2023
Springer Nature B.V |
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| Abstract | In this paper, we will first establish a power saving result for the shifted convolution sums of
k
-th powers and the normalized Fourier coefficients of
SL
2
(
Z
)
cusp forms. Later we will generalize the result to higher rank cases. |
|---|---|
| AbstractList | In this paper, we will first establish a power saving result for the shifted convolution sums of k-th powers and the normalized Fourier coefficients of SL2(Z) cusp forms. Later we will generalize the result to higher rank cases. In this paper, we will first establish a power saving result for the shifted convolution sums of k -th powers and the normalized Fourier coefficients of SL 2 ( Z ) cusp forms. Later we will generalize the result to higher rank cases. |
| Author | Wei, Zhining |
| Author_xml | – sequence: 1 givenname: Zhining orcidid: 0000-0001-7541-3350 surname: Wei fullname: Wei, Zhining email: wei.863@buckeyemail.osu.edu organization: Mathematics Department, Ohio State University |
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| Cites_doi | 10.1215/00127094-2371416 10.1112/jlms/s1-2.3.202 10.11650/tjm.20.2016.7389 10.1093/imrn/rnw083 10.1016/j.aim.2016.02.033 10.1017/CBO9780511470929 10.1017/S030500410200628X 10.1215/S0012-7094-95-07711-4 10.1007/s12188-010-0046-8 10.4007/annals.2016.184.2.7 10.1112/jlms/s2-26.1.1 10.1515/forum-2017-0269 10.1515/crll.1988.384.192 10.1215/00127094-2009-002 10.1093/qmath/os-9.1.199 10.1007/BF01451932 10.1007/s11139-020-00332-4 10.1155/S1073792804142505 10.1215/00127094-2008-038 10.1007/BF02684373 10.1353/ajm.2006.0027 10.1090/pspum/008/0182610 10.1134/S0371968517010034 10.1090/gsm/053 10.24033/ast |
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| Copyright | The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
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| Keywords | Cusp forms Shifted convolution sums Circle method 11P55 11F30 Voronoi formula 11P05 |
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| References | Good (CR23) 1981; 255 Bourgain, Demeter, Guth (CR19) 2016; 184 Iwaniec (CR22) 2002 Ingham (CR1) 1927; 2 CR15 Meurman (CR24) 1988; 384 Wooley (CR18) 2016; 294 Hua (CR16) 1938; 9 Wooley (CR17) 2012; 7 Luo (CR10) 2011; 81 Vaughan (CR14) 1997 Luo (CR13) 2021; 55 Pitt (CR7) 1995; 77 Deshouillers, Iwaniec (CR2) 1982; 26 Blomer, Harcos (CR5) 2008; 144 CR3 Ren, Ye (CR25) 2016; 20 Miller (CR26) 2006; 128 Munshi (CR8) 2013; 162 Sun (CR11) 2017; 6 CR20 Iwaniec (CR21) 1997 Deligne (CR9) 1974; 43 Jiang, Lü (CR12) 2019; 31 Holowinsky (CR6) 2009; 146 Blomer (CR4) 2004; 73 W Luo (677_CR10) 2011; 81 TD Wooley (677_CR17) 2012; 7 J-M Deshouillers (677_CR2) 1982; 26 TD Wooley (677_CR18) 2016; 294 H Iwaniec (677_CR21) 1997 T Meurman (677_CR24) 1988; 384 R Munshi (677_CR8) 2013; 162 AE Ingham (677_CR1) 1927; 2 P Deligne (677_CR9) 1974; 43 Q Sun (677_CR11) 2017; 6 NJE Pitt (677_CR7) 1995; 77 677_CR20 V Blomer (677_CR4) 2004; 73 A Good (677_CR23) 1981; 255 677_CR3 SD Miller (677_CR26) 2006; 128 R Holowinsky (677_CR6) 2009; 146 L-K Hua (677_CR16) 1938; 9 W Luo (677_CR13) 2021; 55 V Blomer (677_CR5) 2008; 144 J Bourgain (677_CR19) 2016; 184 H Iwaniec (677_CR22) 2002 Y Jiang (677_CR12) 2019; 31 677_CR15 X Ren (677_CR25) 2016; 20 RC Vaughan (677_CR14) 1997 |
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Soc. doi: 10.1112/jlms/s1-2.3.202 contributor: fullname: AE Ingham – volume: 255 start-page: 523 issue: 4 year: 1981 ident: 677_CR23 publication-title: Math. Ann. doi: 10.1007/BF01451932 contributor: fullname: A Good – volume: 55 start-page: 1165 issue: 3 year: 2021 ident: 677_CR13 publication-title: Ramanujan J. doi: 10.1007/s11139-020-00332-4 contributor: fullname: W Luo – volume: 77 start-page: 383 issue: 2 year: 1995 ident: 677_CR7 publication-title: Duke Math. J. doi: 10.1215/S0012-7094-95-07711-4 contributor: fullname: NJE Pitt – volume: 144 start-page: 321 issue: 2 year: 2008 ident: 677_CR5 publication-title: Duke Math. J. doi: 10.1215/00127094-2008-038 contributor: fullname: V Blomer – volume: 9 start-page: 199 year: 1938 ident: 677_CR16 publication-title: Quart. J. Math. Oxf. doi: 10.1093/qmath/os-9.1.199 contributor: fullname: L-K Hua – ident: 677_CR20 doi: 10.24033/ast – start-page: 232 volume-title: The Hardy-Littlewood Method year: 1997 ident: 677_CR14 doi: 10.1017/CBO9780511470929 contributor: fullname: RC Vaughan – volume: 384 start-page: 192 year: 1988 ident: 677_CR24 publication-title: J. Reine Angew. Math. doi: 10.1515/crll.1988.384.192 contributor: fullname: T Meurman – volume: 162 start-page: 2345 issue: 13 year: 2013 ident: 677_CR8 publication-title: Duke Math. J. doi: 10.1215/00127094-2371416 contributor: fullname: R Munshi – volume: 184 start-page: 633 issue: 2 year: 2016 ident: 677_CR19 publication-title: Ann. Math. (2) doi: 10.4007/annals.2016.184.2.7 contributor: fullname: J Bourgain – start-page: 259 volume-title: Topics in Classical Automorphic Forms. Graduate Studies in Mathematics year: 1997 ident: 677_CR21 contributor: fullname: H Iwaniec – volume: 128 start-page: 699 issue: 3 year: 2006 ident: 677_CR26 publication-title: Am. J. Math. doi: 10.1353/ajm.2006.0027 contributor: fullname: SD Miller |
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| Snippet | In this paper, we will first establish a power saving result for the shifted convolution sums of
k
-th powers and the normalized Fourier coefficients of
SL
2
(... In this paper, we will first establish a power saving result for the shifted convolution sums of k-th powers and the normalized Fourier coefficients of SL2(Z)... |
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| SubjectTerms | Combinatorics Cusps Field Theory and Polynomials Fourier Analysis Functions of a Complex Variable Mathematics Mathematics and Statistics Number Theory Sums |
| Title | Sums of k-th powers and Fourier coefficients of cusp forms |
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