Li, Peigen Exponential sums and rigid cohomology. (English) Zbl 1496.11138 Finite Fields Appl. 81, Article ID 102031, 16 p. (2022). Reviewer: Dingxin Zhang (Beijing) MSC: 11T23 11L03 14F30 14G22 PDF BibTeX XML Cite \textit{P. Li}, Finite Fields Appl. 81, Article ID 102031, 16 p. (2022; Zbl 1496.11138) Full Text: DOI arXiv
Asakura, Masanori Frobenius action on a hypergeometric curve and an algorithm for computing values of Dwork’s \(p\)-adic hypergeometric functions. (English) Zbl 1499.11354 Bostan, Alin (ed.) et al., Transcendence in algebra, combinatorics, geometry and number theory. TRANS19 – transient transcendence in Transylvania, Brașov, Romania, May 13–17, 2019. Revised and extended contributions. Cham: Springer. Springer Proc. Math. Stat. 373, 1-45 (2021). MSC: 11S80 14H50 14Q05 33E50 PDF BibTeX XML Cite \textit{M. Asakura}, Springer Proc. Math. Stat. 373, 1--45 (2021; Zbl 1499.11354) Full Text: DOI
Haessig, C. Douglas Kloosterman sums and Hecke polynomials in characteristics 2 and 3. (English) Zbl 1475.11142 Finite Fields Appl. 76, Article ID 101896, 14 p. (2021). MSC: 11L05 11S70 11T23 PDF BibTeX XML Cite \textit{C. D. Haessig}, Finite Fields Appl. 76, Article ID 101896, 14 p. (2021; Zbl 1475.11142) Full Text: DOI arXiv
Fried, Michael D. Diophantine statements over residue fields: Galois stratification and uniformity. (English) Zbl 1469.11210 Davis, James A. (ed.), Finite fields and their applications. Proceedings of the 14th international conference on finite fields and their applications (Fq14), Vancouver, Canada, June 3–7, 2019. Berlin: De Gruyter. De Gruyter Proc. Math., 103-132 (2020). MSC: 11G25 11D72 14F30 14G32 PDF BibTeX XML Cite \textit{M. D. Fried}, in: Finite fields and their applications. Proceedings of the 14th international conference on finite fields and their applications (Fq14), Vancouver, Canada, June 3--7, 2019. Berlin: De Gruyter. 103--132 (2020; Zbl 1469.11210) Full Text: DOI
André, Yves; Baldassarri, Francesco; Cailotto, Maurizio De Rham cohomology of differential modules on algebraic varieties. 2nd revised edition. (English) Zbl 1437.14029 Progress in Mathematics 189. Cham: Birkhäuser (ISBN 978-3-030-39718-0/hbk; 978-3-030-39719-7/ebook). xiv, 241 p. (2020). MSC: 14F40 14F10 14-02 13N05 32S40 PDF BibTeX XML Cite \textit{Y. André} et al., De Rham cohomology of differential modules on algebraic varieties. 2nd revised edition. Cham: Birkhäuser (2020; Zbl 1437.14029) Full Text: DOI
Haessig, C. Douglas \(L\)-functions of symmetric powers of Kloosterman sums (unit root \(L\)-functions and \(p\)-adic estimates). (English) Zbl 1405.11114 Math. Ann. 369, No. 1-2, 17-47 (2017). MSC: 11M41 11L05 14F30 14G10 14G15 PDF BibTeX XML Cite \textit{C. D. Haessig}, Math. Ann. 369, No. 1--2, 17--47 (2017; Zbl 1405.11114) Full Text: DOI arXiv
Richard, Rodolphe On \(\pi\)-exponentials. II: Closed formula for the index. (English. French summary) Zbl 1377.12004 J. Théor. Nombres Bordx. 28, No. 2, 539-556 (2016). MSC: 12H25 13F35 14G20 PDF BibTeX XML Cite \textit{R. Richard}, J. Théor. Nombres Bordx. 28, No. 2, 539--556 (2016; Zbl 1377.12004) Full Text: DOI arXiv
Lairez, Pierre Computing periods of rational integrals. (English) Zbl 1337.68301 Math. Comput. 85, No. 300, 1719-1752 (2016). Reviewer: Vladimir P. Kostov (Nice) MSC: 68W30 14K20 14F40 33F10 34M03 PDF BibTeX XML Cite \textit{P. Lairez}, Math. Comput. 85, No. 300, 1719--1752 (2016; Zbl 1337.68301) Full Text: DOI arXiv
Haessig, C. Douglas; Sperber, Steven \(L\)-functions associated with families of toric exponential sums. (English) Zbl 1296.11162 J. Number Theory 144, 422-473 (2014). MSC: 11S40 11T23 PDF BibTeX XML Cite \textit{C. D. Haessig} and \textit{S. Sperber}, J. Number Theory 144, 422--473 (2014; Zbl 1296.11162) Full Text: DOI arXiv
Salerno, Adriana An algorithmic approach to the Dwork family. (English) Zbl 1298.11118 David, Chantal (ed.) et al., Women in numbers 2: Research directions in number theory. Second BIRS workshop WIN2, Banff International Research Station, Banff, Canada, November 6–11, 2011. Providence, RI: American Mathematical Society (AMS); Montreal: Centre de Recherches Mathématiques (CRM) (ISBN 978-1-4704-1022-3/pbk; 978-1-4704-1440-5/ebook). Contemporary Mathematics 606. Centre de Recherches Mathématiques Proceedings, 83-100 (2013). Reviewer: Andreas Stein (Oldenburg) MSC: 11Y16 14G10 33C20 PDF BibTeX XML Cite \textit{A. Salerno}, Contemp. Math. 606, 83--100 (2013; Zbl 1298.11118)
Liu, Chunlei; Liu, Wenxin Twisted exponential sums of polynomials in one variable. (English) Zbl 1275.11112 Sci. China, Math. 53, No. 9, 2395-2404 (2010). Reviewer: John H. Loxton (Greenwich, NSW) MSC: 11L07 11T23 14F30 PDF BibTeX XML Cite \textit{C. Liu} and \textit{W. Liu}, Sci. China, Math. 53, No. 9, 2395--2404 (2010; Zbl 1275.11112) Full Text: DOI arXiv
Shapiro, Ilya Frobenius map on local Calabi-Yau manifolds. (English) Zbl 1202.14021 J. Math. Phys. 50, No. 2, 022302, 14 p. (2009). MSC: 14F40 14J32 PDF BibTeX XML Cite \textit{I. Shapiro}, J. Math. Phys. 50, No. 2, 022302, 14 p. (2009; Zbl 1202.14021) Full Text: DOI arXiv
Adolphson, Alan; Sperber, Steven On the zeta function of a projective complete intersection. (English) Zbl 1232.11092 Ill. J. Math. 52, No. 2, 389-417 (2008). MSC: 11M38 14F30 14G10 PDF BibTeX XML Cite \textit{A. Adolphson} and \textit{S. Sperber}, Ill. J. Math. 52, No. 2, 389--417 (2008; Zbl 1232.11092) Full Text: arXiv Euclid
Candelas, Philip; de la Ossa, Xenia The zeta-function of a \(p\)-adic manifold, Dwork theory for physicists. (English) Zbl 1178.14022 Commun. Number Theory Phys. 1, No. 3, 479-512 (2007). Reviewer: Wilson A. Zuniga-Galindo (México D. F.) MSC: 14G10 11G25 14G15 PDF BibTeX XML Cite \textit{P. Candelas} and \textit{X. de la Ossa}, Commun. Number Theory Phys. 1, No. 3, 479--512 (2007; Zbl 1178.14022) Full Text: DOI arXiv
Lauder, Alan G. B. Counting solutions to equations in many variables over finite fields. (English) Zbl 1076.11040 Found. Comput. Math. 4, No. 3, 221-267 (2004). Reviewer: D. Poulakis (Thessaloniki) MSC: 11G25 14G15 11D45 11M38 11Y16 14F30 PDF BibTeX XML Cite \textit{A. G. B. Lauder}, Found. Comput. Math. 4, No. 3, 221--267 (2004; Zbl 1076.11040) Full Text: DOI
Baldassarri, Francesco; d’Agnolo, Andrea On Dwork cohomology and algebraic \({\mathcal D}\)-modules. (English) Zbl 1061.32022 Adolphson, Alan (ed.) et al., Geometric aspects of Dwork theory. Vol. I, II. Berlin: Walter de Gruyter (ISBN 3-11-017478-2/hbk). 245-253 (2004). Reviewer: Alberto Parmeggiani (Bologna) MSC: 32S40 14F10 PDF BibTeX XML Cite \textit{F. Baldassarri} and \textit{A. d'Agnolo}, in: Geometric aspects of Dwork theory. Vol. I, II. Berlin: Walter de Gruyter. 245--253 (2004; Zbl 1061.32022) Full Text: arXiv
André, Yves; Baldassarri, Francesco De Rham cohomology of differential modules on algebraic varieties. (English) Zbl 0995.14003 Progress in Mathematics (Boston, Mass.). 189. Basel: Birkhäuser. vii, 214 p. (2001). Reviewer: Aleksandr G.Aleksandrov (Moskva) MSC: 14F40 14F10 14-02 13N05 32S40 PDF BibTeX XML Cite \textit{Y. André} and \textit{F. Baldassarri}, De Rham cohomology of differential modules on algebraic varieties. Basel: Birkhäuser (2001; Zbl 0995.14003)
Adolphson, Alan; Sperber, Steven Exponential sums on \(\mathbb{A}^n\). (English) Zbl 1034.11043 Isr. J. Math. 120, Part A, 3-21 (2000). MSC: 11L07 11T23 14F20 14F30 PDF BibTeX XML Cite \textit{A. Adolphson} and \textit{S. Sperber}, Isr. J. Math. 120, Part A, 3--21 (2000; Zbl 1034.11043) Full Text: DOI
Dimca, Alexandru; Maaref, Fayçal; Sabbah, Claude; Saito, Morihiko Dwork cohomology and algebraic \(\mathcal D\)-modules. (English) Zbl 0985.14007 Math. Ann. 318, No. 1, 107-125 (2000). Reviewer: Vasile Brînzănescu (Bucureşti MSC: 14F10 32S40 32C38 14F40 PDF BibTeX XML Cite \textit{A. Dimca} et al., Math. Ann. 318, No. 1, 107--125 (2000; Zbl 0985.14007) Full Text: DOI arXiv
Adolphson, Alan; Sperber, Steven Dwork cohomology, de Rham cohomology, and hypergeometric functions. (English) Zbl 0980.14017 Am. J. Math. 122, No. 2, 319-348 (2000). Reviewer: Aleksandr G.Aleksandrov (Moskva) MSC: 14F40 14F43 14D05 53C05 PDF BibTeX XML Cite \textit{A. Adolphson} and \textit{S. Sperber}, Am. J. Math. 122, No. 2, 319--348 (2000; Zbl 0980.14017) Full Text: DOI arXiv Link
Adolphson, Alan Higher solutions of hypergeometric systems and Dwork cohomology. (English) Zbl 0931.14012 Rend. Semin. Mat. Univ. Padova 101, 179-190 (1999). Reviewer: G.Zet (Iaşi) MSC: 14F40 33C80 14F10 PDF BibTeX XML Cite \textit{A. Adolphson}, Rend. Semin. Mat. Univ. Padova 101, 179--190 (1999; Zbl 0931.14012) Full Text: Numdam EuDML
Garnier, L. Explicit Frobenius descent for \({\mathcal D}^\dagger\)-modules. (Descente par Frobenius explicite pour les \({\mathcal D}^\dagger\)-modules.) (French) Zbl 0926.12006 J. Algebra 205, No. 2, 542-577 (1998). Reviewer: M.Reversat (Toulouse) MSC: 12H25 14F30 14G20 PDF BibTeX XML Cite \textit{L. Garnier}, J. Algebra 205, No. 2, 542--577 (1998; Zbl 0926.12006) Full Text: DOI
Adolphson, Alan; Sperber, Steven Differential modules defined by systems of equations. (English) Zbl 0944.12003 Rend. Semin. Mat. Univ. Padova 95, 37-57 (1996). Reviewer: M.van der Put (Groningen) MSC: 12H05 13N10 52B20 PDF BibTeX XML Cite \textit{A. Adolphson} and \textit{S. Sperber}, Rend. Semin. Mat. Univ. Padova 95, 37--57 (1996; Zbl 0944.12003) Full Text: Numdam EuDML
Adolphson, Alan; Sperber, Steven On the zeta function of a complete intersection. (English) Zbl 0911.11030 Ann. Sci. Éc. Norm. Supér. (4) 29, No. 3, 287-328 (1996). MSC: 11G25 14G10 14G15 19F27 14C17 PDF BibTeX XML Cite \textit{A. Adolphson} and \textit{S. Sperber}, Ann. Sci. Éc. Norm. Supér. (4) 29, No. 3, 287--328 (1996; Zbl 0911.11030) Full Text: DOI Numdam Numdam EuDML
Wan, Daqing Meromorphic continuation of \(L\)-functions of \(p\)-adic representations. (English) Zbl 0868.14011 Ann. Math. (2) 143, No. 3, 469-498 (1996). Reviewer: D.Goss (Columbus/Ohio) MSC: 14F30 14G10 PDF BibTeX XML Cite \textit{D. Wan}, Ann. Math. (2) 143, No. 3, 469--498 (1996; Zbl 0868.14011) Full Text: DOI
Mebkhout, Z.; Narváez-Macarro, L. Theory of the Bernstein-Sato polynomial for Tate and Dwork-Monsky-Washnitzer algebras. (La théorie du polynôme de Bernstein-Sato pour les algèbres de Tate et de Dwork-Monsky-Washnitzer.) (French) Zbl 0765.14009 Ann. Sci. Éc. Norm. Supér. (4) 24, No. 2, 227-256 (1991). Reviewer: K.Kiyek (Paderborn) MSC: 14F10 14F40 32C38 14G20 PDF BibTeX XML Cite \textit{Z. Mebkhout} and \textit{L. Narváez-Macarro}, Ann. Sci. Éc. Norm. Supér. (4) 24, No. 2, 227--256 (1991; Zbl 0765.14009) Full Text: DOI Numdam EuDML
Carpentier, Michel Exponential sums the geometry of which is very beautiful: \(p\)-adic estimates. (Sommes exponentielles dont la géométrie est très belle: \(p\)-adic estimates.) (French) Zbl 0749.14014 Pac. J. Math. 141, No. 2, 229-277 (1990). Reviewer: F.Herrlich (Karlsruhe) MSC: 14G10 14G15 11L05 11L07 PDF BibTeX XML Cite \textit{M. Carpentier}, Pac. J. Math. 141, No. 2, 229--277 (1990; Zbl 0749.14014) Full Text: DOI
Adolphson, Alan; Sperber, Steven Exponential sums and Newton polyhedra: cohomology and estimates. (English) Zbl 0723.14017 Ann. Math. (2) 130, No. 2, 367-406 (1989). Reviewer: F. Baldassarri (Padova) MSC: 14G10 11T23 14G15 11L40 14M25 PDF BibTeX XML Cite \textit{A. Adolphson} and \textit{S. Sperber}, Ann. Math. (2) 130, No. 2, 367--406 (1989; Zbl 0723.14017) Full Text: DOI
Robba, Philippe Une introduction naïve aux cohomologies de Dwork. (A naïve introduction to Dwork cohomology). (French) Zbl 0623.14005 Mém. Soc. Math. Fr., Nouv. Sér. 23, 61-105 (1986). Reviewer: M.van der Put MSC: 14F30 14G20 PDF BibTeX XML Cite \textit{P. Robba}, Mém. Soc. Math. Fr., Nouv. Sér. 23, 61--105 (1986; Zbl 0623.14005) Full Text: DOI Numdam EuDML
Robba, Philippe Symmetric powers of the p-adic Bessel equation. (English) Zbl 0574.12021 J. Reine Angew. Math. 366, 194-220 (1986). MSC: 12H25 14F30 11L03 PDF BibTeX XML Cite \textit{P. Robba}, J. Reine Angew. Math. 366, 194--220 (1986; Zbl 0574.12021) Full Text: DOI Crelle EuDML
Carpentier, Michel J. Cohomologie des fonctions \(_ 0F_ n\). (Cohomology of the functions \(_ 0F_ n)\). (French) Zbl 0589.12022 Groupe Étude Anal. Ultramétrique 12e année 1984/85, No. 1, Exposé No. 9, 10 p. (1985). MSC: 12H25 14F30 33C60 11L40 11T23 PDF BibTeX XML Full Text: Numdam EuDML
Robba, Philippe Produit symétrique de l’équation de Bessel. (Symmetric product of the Bessel equation). (French) Zbl 0582.12013 Groupe Étude Anal. Ultramétrique 12 e année 1984/85, No. 1, Exposé No. 7, 3 p. (1985). MSC: 12H25 14F30 11L03 PDF BibTeX XML Full Text: Numdam EuDML
Berthelot, Pierre Cohomologie rigide et théorie de Dwork: Le cas des sommes exponentielles. (French) Zbl 0577.14013 Cohomologie p-adique, Astérisque 119/120, 17-49 (1984). Reviewer: F.Herrlich MSC: 14F30 14F40 14G20 PDF BibTeX XML
Boyarsky, Maurizio [Fresnel, Jean] The Reich trace formula. Appendice: Une base normale pour l’algèbre de Banach de Reich by Jean Fresnel. (English) Zbl 0561.12013 Cohomologie p-adique, Astérisque 119/120, 129-150 (1984). Reviewer: M.van der Put MSC: 12J27 14G20 14F30 PDF BibTeX XML
Adolphson, Alan; Sperber, Steven Twisted Kloosterman sums and \(p\)-adic Bessel functions. (English) Zbl 0552.12010 Am. J. Math. 106, 549-591 (1984). Reviewer: Francesco Baldassarri (Padova) MSC: 12H25 11S80 14F30 11S40 11L05 PDF BibTeX XML Cite \textit{A. Adolphson} and \textit{S. Sperber}, Am. J. Math. 106, 549--591 (1984; Zbl 0552.12010) Full Text: DOI
Baldassarri, Francesco Higher p-adic gamma functions and Dwork cohomology. (English) Zbl 0551.12012 Cohomologie p-adique, Astérisque 119-120, 111-127 (1984). MSC: 11S80 14F30 PDF BibTeX XML
Dwork, Bernard A note on the \(p\)-adic gamma function. (English) Zbl 0512.12013 Groupe Étude Anal. Ultramétrique 9e Année: 1981/82, No. 3, Exp. No. J5, 10 p. (1983). Reviewer: Gilles Christol (Paris) MSC: 11S80 11F85 14F30 33E50 PDF BibTeX XML Full Text: Numdam EuDML