Mathscinet   (Providence site;   Rice mirror site)  (Note: The list of journal links below contains links not found in Mathscinet, and contains free links in several cases where Mathscinet contains non-free links.)
Jahrbuch über die Fortschritte der Mathematik (reviews of math papers 1868–1942)
Zentralblatt MATH (reviews of math papers 1931–present; a sample search is au:zieve & ti:polynomial* ^an:pre05567227

Math arXiv  (papers;   e-mail alert;   paper submission)

Springer Lecture Notes in Mathematics
Springer Lecture Notes in Computer Science
(Many other Springer-published books and conference proceedings are also available on Springer's website; click on the item, then "read online'', then look up a chapter and you'll be able to download the pdf, usually from a link on the rightmost part of the bar atop the displayed page.)
Buy Springer books via MyCopy

7FAST (Free service includes both interlibrary loan and the scanning of any article or book chapter of an item in our library)
Mirlyn (Search UMich library)

Math websites
Number Theory Web  
Conferences in  number theory   or   arithmetic geometry

Electronic journals with number theory content:  (more e-journals listed here and here)
(Unless otherwise noted, UMich has full electronic runs of each journal, and has hard copy of all issues not available electronically)
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg
Acta Arithmetica (volumes 96–present) (volumes 1–95)
Acta Mathematica
Acta Mathematica Hungarica (since March 1983)
Acta Mathematica Sinica (New (English) series)
Advances in Mathematics
Aequationes Mathematicae
Algebra & Number Theory
Algebra Colloquium (latest five years) (vol.7 numbers 1–3, vol. 10 number 1)
Algorithmica
American Journal of Mathematics (volumes 118–present) (volumes 1–117)
American Mathematical Monthly
Annales Academiae Scientiarum Fennicae. Mathematica (volumes 18–present)
Annales de l'Institut Fourier (Grenoble)
Annales Polonici Mathematici (volumes 76–present) (volumes 1–11 and 74–75)
Annales scientifiques de l'École Normale Supérieure
Annali della Scuola Normale Superiore di Pisa, Classe di Scienze (1871–2003)
Annali di Matematica Pura ed Applicata
Annals of Combinatorics
Annals of Mathematics (1999–present) (older issues)
Applicable Algebra in Engineering, Communication and Computing
Archiv der Mathematik
Arkiv för Matematik
Asian Journal of Algebra
Asian Journal of Mathematics (volumes 8–present)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Serie IX. Matematica e Applicazioni (volumes 17–present) (volumes 9–16)
Australasian Journal of Combinatorics (all issues from at least four years ago)
Bulletin de la Société Mathematique de France
Bulletin des sciences Mathématiques (volumes 122–present)
Bulletin of the American Mathematical Society
Bulletin of the Australian Mathematical Society
Bulletin of the Belgian Mathematical Society – Simon Stevin
Bulletin of the London Mathematical Society
Canadian Journal of Mathematics
Canadian Mathematical Bulletin (volumes 40–present)
Colloquium Mathematicum (volumes 87–present) (volumes 1–11 and 62–75)
Combinatorica
Commentarii Mathematici Helvetici (since 1997) (older issues)
Communications in Algebra (volumes 33–37) (UMich has hard copy of volumes 1–37)
Communications on Pure and Applied Mathematics
Compositio Mathematica (volumes 105–present) (volumes 51–104) (volumes 1–50)
Comptes Rendus Mathematique (volumes 334–present)
Comptes Rendus de l'Académie des Sciences. Série I, Mathématique (volumes 324–333) (volumes 298–323) (volumes 293–296)
Comptes Rendus Hebdomadaires des Séances de l'Académie des Sciences. Série A et B: Sciences Mathématiques. Sciences Physiques (volumes 284–291) (volumes 266–275) (volumes 1–261)
Computational Complexity
Designs, Codes, and Cryptography
Discrete Mathematics
Doklady Mathematics (volumes 73–present)
Duke Mathematical Journal
Electronic Journal of Combinatorics
L'Enseignement Mathématique
European Journal of Combinatorics
Experimental Mathematics
Expositiones Mathematicae (volumes 19–present)
Finite Fields and their Applications
Forum Mathematicum (volumes 10–present) (volumes 1–9)
Functional Analysis and its Applications
Functiones et Approximatio Commentarii Mathematici (volumes 35–present) (volumes 28–34)
Geometric and Functional Analysis
IEEE Transactions on Information Theory (volumes 9–present) (volumes 1–8)
Illinois Journal of Mathematics
Indagationes Mathematicae (since 1990) (volumes 72–92)
INTEGERS: Electronic Journal of Combinatorial Number Theory (note: they provide pdf files with cgi filenames, which confuses some web browsers; if this happens, save the files and view then with a pdf viewer)
International Journal of Algebra and Computation (volumes 11–present)
International Journal of Mathematics (last five years) (UMich has hard copy of all issues)
International Journal of Mathematics and Mathematical Sciences
International Mathematics Research Notices
Inventiones Mathematicae
Israel Journal of Mathematics
Izvestiya. Mathematics
Journal de Mathématiques Pures et Appliquées (volumes 76–present) (some earlier volumes) (more earlier volumes)
Journal de Théorie des Nombres de Bordeaux (continues Seminaire de Théorie des Nombres de Bordeaux)
Journal für die reine und angewandte Mathematik (Crelle's journal) (volumes 494–present) (volumes 1–493)
Journal of Algebra
Journal of Algebraic Geometry (volumes 11–present)
Journal of Algorithms
Journal of Combinatorial Theory. Series A
Journal of Combinatorial Theory
Journal of Geometry
Journal of Group Theory
Journal of Number Theory
Journal of Pure and Applied Algebra
Journal of Mathematical Sciences (formerly Journal of Soviet Mathematics)
Journal of Symbolic Computation
Journal of the American Mathematical Society
Journal of the Australian Mathematical Society
Journal of the European Mathematical Society
Journal of the Institute of Mathematics of Jussieu
Journal of the London Mathematical Society
Journal of the Ramanujan Mathematical Society (no online access, but UMich has hard copy)
Journal of Topology
K-Theory
L'Enseignement Mathématique (volumes 1–52)
Linear & Multilinear Algebra (volumes 53–57) (UMich has hard copy of volumes 1–57)
Linear Algebra and its Applications
Manuscripta Mathematica
Mathematica Scandinavica (volumes 1–81)
Mathematical Intelligencer
Mathematical Journal of Okayama University (volumes 46–present)
Mathematical Notes
Mathematical Proceedings of the Cambridge Philosophical Society (unfortunately UMich does not provide e-access, but does have the paper version of this journal)
Mathematical Research Letters
Mathematics of Computation
Mathematics of the USSR. Sbornik
Mathematics of the USSR. Izvestija
Mathematika (unfortunately UMich does not provide e-access, but does have the paper version of this journal)
Mathematische Annalen
Mathematische Nachrichten
Mathematische Zeitschrift
Messenger of Mathematics
Michigan Mathematical Journal
Monatshefte für Mathematik
Moscow Mathematical Journal
Nagoya Mathematical Journal
New York Journal of Mathematics
New Zealand Journal of Mathematics (volumes 36–present)
Nonlinearity
Notices of the American Mathematical Society (volumes 42–present)
Oberwolfach reports
Pacific Journal of Mathematics (volumes 177–present) (volumes 1–176)
Periodica Mathematica Hungarica
Proceedings of the American Mathematical Society
Proceedings of the Japan Academy. Series A: Mathematical Sciences (volumes 53–present)
Proceedings of the London Mathematical Society
Proceedings of the National Academy of Sciences
Proceedings of the Steklov Institute of Mathematics (volumes 252–present)
Publicationes Mathematicae Debrecen (volumes 39–present)
Publications of the Research Institute for Mathematical Sciences (PRIMS)
Quarterly Journal of Mathematics
Ramanujan Journal
Rendiconti del Seminario Matematico della Università di Padova
Rendiconti Lincei. Matematica e Applicazioni (volumes 17–present) (volumes 9–16)
Rocky Mountain Journal of Mathematics (volumes 20–present)
Russian Mathematical Surveys (Uspekhi Matematischeskikh Nauk) (volumes 15–present)
Russian Mathematics (Iz. VUZ) (volumes 51–present)
Sbornik. Mathematics
Seminaire de Théorie des Nombres de Bordeaux (continued by Journal de Théorie des Nombres de Bordeaux, which was originally called series 2 of this journal)
Séminaire Delange–Pisot–Poitou (volumes 1–20)
Tôhoku Mathematical Journal
Topology
Transactions of the American Mathematical Society
(Unless otherwise noted, UMich has full electronic runs of each journal listed above, and has hard copy of all issues not available electronically)

Please email zieve[at]umich.edu if you spot any mistakes, or know of other useful journals!