On exponential sums of

Let ψ be a character of Z p of order p...
Ausführliche Beschreibung

Let ψ be a character of Z p of order p m , and f ( x ) = x d + λ x e be a binomial of degree d with ( d , e ) = 1 . The determination of the Newton slopes of the L-functions L f , ψ ( s ) is interesting and still open for general d , e that coprime. If p ≡ e ( mod d ) is large enough, an arithmetic polygon P e , d is defined and shown to be the lower bound for the classical ( ψ ( 1 ) − 1 ) a ( p − 1 ) -adic Newton polygon of L f , ψ ( s ) . In addition, we show they coincide when e = 2 for large p, hence the Newton slopes of L f , ψ ( s ) are determined. Combining Ouyang-Zhang's results on e = d − 1 and p ≡ d − 1 ( mod d ) , we conjecture P e , d coincides with ( ψ ( 1 ) − 1 ) a ( p − 1 ) -adic Newton polygon of L f , ψ ( s ) for all e if p ≡ e ( mod d ) is large enough. Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Zhang, Qingjie [verfasserIn] Niu, Chuanze [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2021

Schlagwörter:	Exponential sums Newton polygons

Übergeordnetes Werk:	Enthalten in: No title available - 76
Übergeordnetes Werk:	volume:76

DOI / URN:	10.1016/j.ffa.2021.101907

Katalog-ID:	ELV006779816

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520			\|a Let ψ be a character of Z p of order p m , and f ( x ) = x d + λ x e be a binomial of degree d with ( d , e ) = 1 . The determination of the Newton slopes of the L-functions L f , ψ ( s ) is interesting and still open for general d , e that coprime. If p ≡ e ( mod d ) is large enough, an arithmetic polygon P e , d is defined and shown to be the lower bound for the classical ( ψ ( 1 ) − 1 ) a ( p − 1 ) -adic Newton polygon of L f , ψ ( s ) . In addition, we show they coincide when e = 2 for large p, hence the Newton slopes of L f , ψ ( s ) are determined. Combining Ouyang-Zhang's results on e = d − 1 and p ≡ d − 1 ( mod d ) , we conjecture P e , d coincides with ( ψ ( 1 ) − 1 ) a ( p − 1 ) -adic Newton polygon of L f , ψ ( s ) for all e if p ≡ e ( mod d ) is large enough.
650		4	\|a Exponential sums
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allfields	10.1016/j.ffa.2021.101907 doi (DE-627)ELV006779816 (ELSEVIER)S1071-5797(21)00101-5 DE-627 ger DE-627 rda eng Zhang, Qingjie verfasserin aut On exponential sums of 2021 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Let ψ be a character of Z p of order p m , and f ( x ) = x d + λ x e be a binomial of degree d with ( d , e ) = 1 . The determination of the Newton slopes of the L-functions L f , ψ ( s ) is interesting and still open for general d , e that coprime. If p ≡ e ( mod d ) is large enough, an arithmetic polygon P e , d is defined and shown to be the lower bound for the classical ( ψ ( 1 ) − 1 ) a ( p − 1 ) -adic Newton polygon of L f , ψ ( s ) . In addition, we show they coincide when e = 2 for large p, hence the Newton slopes of L f , ψ ( s ) are determined. Combining Ouyang-Zhang's results on e = d − 1 and p ≡ d − 1 ( mod d ) , we conjecture P e , d coincides with ( ψ ( 1 ) − 1 ) a ( p − 1 ) -adic Newton polygon of L f , ψ ( s ) for all e if p ≡ e ( mod d ) is large enough. Exponential sums Newton polygons Niu, Chuanze verfasserin aut Enthalten in No title available 76 (DE-627)26687701X 1071-5797 nnns volume:76 GBV_USEFLAG_U SYSFLAG_U GBV_ELV GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_224 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 AR 76
spelling	10.1016/j.ffa.2021.101907 doi (DE-627)ELV006779816 (ELSEVIER)S1071-5797(21)00101-5 DE-627 ger DE-627 rda eng Zhang, Qingjie verfasserin aut On exponential sums of 2021 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Let ψ be a character of Z p of order p m , and f ( x ) = x d + λ x e be a binomial of degree d with ( d , e ) = 1 . The determination of the Newton slopes of the L-functions L f , ψ ( s ) is interesting and still open for general d , e that coprime. If p ≡ e ( mod d ) is large enough, an arithmetic polygon P e , d is defined and shown to be the lower bound for the classical ( ψ ( 1 ) − 1 ) a ( p − 1 ) -adic Newton polygon of L f , ψ ( s ) . In addition, we show they coincide when e = 2 for large p, hence the Newton slopes of L f , ψ ( s ) are determined. Combining Ouyang-Zhang's results on e = d − 1 and p ≡ d − 1 ( mod d ) , we conjecture P e , d coincides with ( ψ ( 1 ) − 1 ) a ( p − 1 ) -adic Newton polygon of L f , ψ ( s ) for all e if p ≡ e ( mod d ) is large enough. Exponential sums Newton polygons Niu, Chuanze verfasserin aut Enthalten in No title available 76 (DE-627)26687701X 1071-5797 nnns volume:76 GBV_USEFLAG_U SYSFLAG_U GBV_ELV GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_224 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 AR 76
allfields_unstemmed	10.1016/j.ffa.2021.101907 doi (DE-627)ELV006779816 (ELSEVIER)S1071-5797(21)00101-5 DE-627 ger DE-627 rda eng Zhang, Qingjie verfasserin aut On exponential sums of 2021 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Let ψ be a character of Z p of order p m , and f ( x ) = x d + λ x e be a binomial of degree d with ( d , e ) = 1 . The determination of the Newton slopes of the L-functions L f , ψ ( s ) is interesting and still open for general d , e that coprime. If p ≡ e ( mod d ) is large enough, an arithmetic polygon P e , d is defined and shown to be the lower bound for the classical ( ψ ( 1 ) − 1 ) a ( p − 1 ) -adic Newton polygon of L f , ψ ( s ) . In addition, we show they coincide when e = 2 for large p, hence the Newton slopes of L f , ψ ( s ) are determined. Combining Ouyang-Zhang's results on e = d − 1 and p ≡ d − 1 ( mod d ) , we conjecture P e , d coincides with ( ψ ( 1 ) − 1 ) a ( p − 1 ) -adic Newton polygon of L f , ψ ( s ) for all e if p ≡ e ( mod d ) is large enough. Exponential sums Newton polygons Niu, Chuanze verfasserin aut Enthalten in No title available 76 (DE-627)26687701X 1071-5797 nnns volume:76 GBV_USEFLAG_U SYSFLAG_U GBV_ELV GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_224 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 AR 76
allfieldsGer	10.1016/j.ffa.2021.101907 doi (DE-627)ELV006779816 (ELSEVIER)S1071-5797(21)00101-5 DE-627 ger DE-627 rda eng Zhang, Qingjie verfasserin aut On exponential sums of 2021 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Let ψ be a character of Z p of order p m , and f ( x ) = x d + λ x e be a binomial of degree d with ( d , e ) = 1 . The determination of the Newton slopes of the L-functions L f , ψ ( s ) is interesting and still open for general d , e that coprime. If p ≡ e ( mod d ) is large enough, an arithmetic polygon P e , d is defined and shown to be the lower bound for the classical ( ψ ( 1 ) − 1 ) a ( p − 1 ) -adic Newton polygon of L f , ψ ( s ) . In addition, we show they coincide when e = 2 for large p, hence the Newton slopes of L f , ψ ( s ) are determined. Combining Ouyang-Zhang's results on e = d − 1 and p ≡ d − 1 ( mod d ) , we conjecture P e , d coincides with ( ψ ( 1 ) − 1 ) a ( p − 1 ) -adic Newton polygon of L f , ψ ( s ) for all e if p ≡ e ( mod d ) is large enough. Exponential sums Newton polygons Niu, Chuanze verfasserin aut Enthalten in No title available 76 (DE-627)26687701X 1071-5797 nnns volume:76 GBV_USEFLAG_U SYSFLAG_U GBV_ELV GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_224 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 AR 76
allfieldsSound	10.1016/j.ffa.2021.101907 doi (DE-627)ELV006779816 (ELSEVIER)S1071-5797(21)00101-5 DE-627 ger DE-627 rda eng Zhang, Qingjie verfasserin aut On exponential sums of 2021 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Let ψ be a character of Z p of order p m , and f ( x ) = x d + λ x e be a binomial of degree d with ( d , e ) = 1 . The determination of the Newton slopes of the L-functions L f , ψ ( s ) is interesting and still open for general d , e that coprime. If p ≡ e ( mod d ) is large enough, an arithmetic polygon P e , d is defined and shown to be the lower bound for the classical ( ψ ( 1 ) − 1 ) a ( p − 1 ) -adic Newton polygon of L f , ψ ( s ) . In addition, we show they coincide when e = 2 for large p, hence the Newton slopes of L f , ψ ( s ) are determined. Combining Ouyang-Zhang's results on e = d − 1 and p ≡ d − 1 ( mod d ) , we conjecture P e , d coincides with ( ψ ( 1 ) − 1 ) a ( p − 1 ) -adic Newton polygon of L f , ψ ( s ) for all e if p ≡ e ( mod d ) is large enough. Exponential sums Newton polygons Niu, Chuanze verfasserin aut Enthalten in No title available 76 (DE-627)26687701X 1071-5797 nnns volume:76 GBV_USEFLAG_U SYSFLAG_U GBV_ELV GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_224 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 AR 76
language	English
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author	Zhang, Qingjie
spellingShingle	Zhang, Qingjie misc Exponential sums misc Newton polygons On exponential sums of
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topic_title	On exponential sums of Exponential sums Newton polygons
topic	misc Exponential sums misc Newton polygons
topic_unstemmed	misc Exponential sums misc Newton polygons
topic_browse	misc Exponential sums misc Newton polygons
format_facet	Elektronische Aufsätze Aufsätze Elektronische Ressource
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title	On exponential sums of
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title_full	On exponential sums of
author_sort	Zhang, Qingjie
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author_browse	Zhang, Qingjie Niu, Chuanze
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format_se	Elektronische Aufsätze
author-letter	Zhang, Qingjie
doi_str_mv	10.1016/j.ffa.2021.101907
author2-role	verfasserin
title_sort	on exponential sums of
title_auth	On exponential sums of
abstract	Let ψ be a character of Z p of order p m , and f ( x ) = x d + λ x e be a binomial of degree d with ( d , e ) = 1 . The determination of the Newton slopes of the L-functions L f , ψ ( s ) is interesting and still open for general d , e that coprime. If p ≡ e ( mod d ) is large enough, an arithmetic polygon P e , d is defined and shown to be the lower bound for the classical ( ψ ( 1 ) − 1 ) a ( p − 1 ) -adic Newton polygon of L f , ψ ( s ) . In addition, we show they coincide when e = 2 for large p, hence the Newton slopes of L f , ψ ( s ) are determined. Combining Ouyang-Zhang's results on e = d − 1 and p ≡ d − 1 ( mod d ) , we conjecture P e , d coincides with ( ψ ( 1 ) − 1 ) a ( p − 1 ) -adic Newton polygon of L f , ψ ( s ) for all e if p ≡ e ( mod d ) is large enough.
abstractGer	Let ψ be a character of Z p of order p m , and f ( x ) = x d + λ x e be a binomial of degree d with ( d , e ) = 1 . The determination of the Newton slopes of the L-functions L f , ψ ( s ) is interesting and still open for general d , e that coprime. If p ≡ e ( mod d ) is large enough, an arithmetic polygon P e , d is defined and shown to be the lower bound for the classical ( ψ ( 1 ) − 1 ) a ( p − 1 ) -adic Newton polygon of L f , ψ ( s ) . In addition, we show they coincide when e = 2 for large p, hence the Newton slopes of L f , ψ ( s ) are determined. Combining Ouyang-Zhang's results on e = d − 1 and p ≡ d − 1 ( mod d ) , we conjecture P e , d coincides with ( ψ ( 1 ) − 1 ) a ( p − 1 ) -adic Newton polygon of L f , ψ ( s ) for all e if p ≡ e ( mod d ) is large enough.
abstract_unstemmed	Let ψ be a character of Z p of order p m , and f ( x ) = x d + λ x e be a binomial of degree d with ( d , e ) = 1 . The determination of the Newton slopes of the L-functions L f , ψ ( s ) is interesting and still open for general d , e that coprime. If p ≡ e ( mod d ) is large enough, an arithmetic polygon P e , d is defined and shown to be the lower bound for the classical ( ψ ( 1 ) − 1 ) a ( p − 1 ) -adic Newton polygon of L f , ψ ( s ) . In addition, we show they coincide when e = 2 for large p, hence the Newton slopes of L f , ψ ( s ) are determined. Combining Ouyang-Zhang's results on e = d − 1 and p ≡ d − 1 ( mod d ) , we conjecture P e , d coincides with ( ψ ( 1 ) − 1 ) a ( p − 1 ) -adic Newton polygon of L f , ψ ( s ) for all e if p ≡ e ( mod d ) is large enough.
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title_short	On exponential sums of
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doi_str	10.1016/j.ffa.2021.101907
up_date	2024-07-06T22:32:10.916Z
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The determination of the Newton slopes of the L-functions L f , ψ ( s ) is interesting and still open for general d , e that coprime. If p ≡ e ( mod d ) is large enough, an arithmetic polygon P e , d is defined and shown to be the lower bound for the classical ( ψ ( 1 ) − 1 ) a ( p − 1 ) -adic Newton polygon of L f , ψ ( s ) . In addition, we show they coincide when e = 2 for large p, hence the Newton slopes of L f , ψ ( s ) are determined. Combining Ouyang-Zhang's results on e = d − 1 and p ≡ d − 1 ( mod d ) , we conjecture P e , d coincides with ( ψ ( 1 ) − 1 ) a ( p − 1 ) -adic Newton polygon of L f , ψ ( s ) for all e if p ≡ e ( mod d ) is large enough.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Exponential sums</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Newton polygons</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Niu, Chuanze</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">No title available</subfield><subfield code="g">76</subfield><subfield code="w">(DE-627)26687701X</subfield><subfield code="x">1071-5797</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:76</subfield></datafield><datafield 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